Curriculum vitae et studiorum PERSONAL DATA. Post-doc position, Centro de Matemática (CMUC), University of Coimbra, Portugal.

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1 Agnese Di Castro H T B agnese.dicastro@gmail.com agnese.dicastro@unipr.it Curriculum vitae et studiorum PERSONAL DATA Address Via Monte Fumaiolo Rome (Italy). Nationality Italian. Place and date of birth Rome, 12th July Homepage EDUCATION AND CURRENT POSITION September 2011-July 2013 Post-doc position (ERC grant Vectorial Elliptic, Parabolic and Variational Problems: Singularities and Regularity, Principal Investigator: Prof. Giuseppe Mingione), Dipartimento di Matematica e Informatica, University of Parma, Italy. November 2009-August 2011 Post-doc position, Centro de Matemática (CMUC), University of Coimbra, Portugal. September 2009-October 2009 Contracto de Investigación (Post doctoral fellow), Departamento de Análisis Matemático, University of Granada, Spain. April 2009-August 2009 Post-doc position, Dipartimento di Matematica, Sapienza, University of Rome, Italy. 16th December 2008 Ph. D. in Mathematics, Sapienza, University of Rome, Italy. 1/16

2 title supervisor thesis committee Elliptic problems for some anisotropic operators. Prof. Lucio Boccardo. Prof. Nicola Fusco, University of Naples "Federico II"; Prof. Maria Michaela Porzio, Sapienza, University of Rome; Prof. José Miguel Urbano, University of Coimbra. November 2004-October 2008 Doctoral fellowship in Pure Mathematics (XX ciclo), Sapienza, University of Rome, Italy. 28th September 2004 final grade title advisor Degree in Pure Mathematics, Sapienza, University of Rome, Italy. 110/110 Cum laude. Existence and summability results for some elliptic problems. Prof. Lucio Boccardo. 14th July 2000 final grade 100/100. High school diploma, Nomentano, secondary school, Rome, Italy. EXPERIENCE Teaching a. y Assistant Professor, of Prof. Giuseppe Mingione, University of Parma, Italy. Mathematical Analysis I, to Engineering degree. a. y Assistant Professor, of Prof. Andrea Dall Aglio and Prof. Daniela Sforza, Sapienza, University of Rome, Italy. Mathematical Analysis II, to Aerospace Engineering degree. a. y Assistant Professor, of Prof. Andrea Dall Aglio, Sapienza, University of Rome, Italy. Mathematical Analysis I, to Aerospace Engineering degree. a. y Assistant Professor, of Prof. Lucio Boccardo and Prof. Andrea Terracina, Sapienza, University of Rome, Italy. Calculus I, to Math degree. 2/16

3 a. y Assistant Professor, of Prof. Laura Tedeschini Lalli and Prof. Paola Magrone, University of Rome III, Italy. Institution of Mathematics II, to Architecture degree. a. y Assistant Professor, of Prof. Angela Pistoia and Prof. Tommaso Leonori, Sapienza, University of Rome, Italy. Mathematical Analysis I, to Clinical Engineering degree. a. y Assistant Professor, of Prof. Adriano Pisante, Sapienza, University of Rome, Italy. Differential Calculus, to Computer Science degree. Other work experiences a. y Editorial board (Proceedings of the International Workshop New Trends in Nonlinear Parabolic Equations ), in Rivista di Matematica dell Università di Parma, in collaboration with G. Mingione and G. Palatucci, University of Parma, Italy. a. y Collaboration fellowship at Library of Mathematics, Sapienza University of Rome, Department "G. Castelnuovo", Italy. February 20-22, 2013 INTERNATIONAL CONFERENCES AND COURSES Winter School on Fast and Anomalous Diffusion. Sapienza, University of Rome, Italy. December 11-12, 2012 Norwegian-Italian Workshop in PDE s. NTNU, Trondheim, Norway. July 1-6, 2012 Recent Trends in Nonlinear Diffusion. Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy. June 24-29, 2012 Topics in Nonlinear Parabolic Equations. Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy. 3/16

4 May 28-June 1, 2012 Workshop on Nonlinear Partial Differential Equations on the occasion of the sixtieth birthday of Patrizia Pucci. Dipartimento di Matematica e Informatica, Perugia, Italy. May 10-12, 2012 Young women in PDEs. Institute for Applied Mathematics, Bonn, Germany. March 1-3, 2012 Trends in Mathematical Analysis. "Francesco Brioschi", Mathematics Department, Politecnico di Milano, Milan, Italy. January 17-20, 2012 A week on Fractional Diffusion. Mathematics Department, Politecnico di Milano, Milan, Italy. August 15-19, 2011 Frontiers of Mathematics and Applications Summer Course UIMP Santander, Spain. June 27-July 1, 2011 Ninth "Jornades d introducció als sistemes dinàmics i a les EDP s" (JISD 2011). Universitat Politécnica de Catalunya (UPC), Barcelona, Spain. June 13-17, 2011 Aubry-Mather theory and Optimal Transport Summer School. Instituto Superior Técnico, Lisbon, Portugal. May 18-20, 2011 Segundas Jornadas de Análisis Matemático en Alicante (πjama), (Second Workshop in Mathematical Analysis in Alicante). Alicante, Spain. June 8-11, 2010 Nonlinear evolution equations. Hotel "Conchiglia d Oro", Mondello, Palermo, Italy. February 9-13, 2009 XIX Convegno Nazionale di Calcolo delle Variazioni. Organized by C.I.R.M. and by Mathematics Department, University of Trento, Levico Terme (Trento), Italy. January 23-24, 2009 Workshop on calculus of variations and PDE s. Mathematics Department "Ulisse Dini", University of Florence, Italy. June 18-20, 2008 Workshop on elliptic and parabolic equations and systems. University of Naples "Federico II", Italy. 4/16

5 May 26-30, 2008 Spring School in Nonlinear Partial Differential Equations. Catholic University of Louvain, Louvain-la-Neuve, Belgium. April 07-11, 2008 Topics in PDE s and applications A CRM and FISYMAT Joint activity, Granada, Spain. September 17-19, 2007 Primer encuentro de la Red de Ecuaciones Parabolicas y Elipticas no lineales. San José, Nìjar, Almeria, Spain. July 22-27, 2007 Topics in Nonlinear PDE s. CIM/UC Summer School, Coimbra, Portugal. June 26-29, 2007 Non-linear diffusion: Mathematics and Applications. International conference in honour of Juan Luis Vazquez on the occasion of his 60th birthday, El Escorial, Madrid, Spain. June 07-10, 2007 Qualitative properties of solutions to Elliptic and Parabolic Equations. European Science Foundation Program, Workshop/Summer School in Saariselkä, Finland. February 12-15, 2007 Recent trends in Nonlinear Partial Differential Equations. Workshop in occasion of the 60th birthday of Ireneo Peral, Salamanca, Spain. October 30 - November 1, 2006 Renormalisation en EDP and Applications. Workshop ENSAM, Meknes, Morocco. June 19-21, 2006 Espalia Mathematics Department, Sapienza, University of Rome, Italy. June 05-09, 2006 Third Summer School in Analysis and Applied Mathematics. Mathematics Department, Sapienza, University of Rome, Italy. February 05-10, 2006 Giornate di Lavoro su Questioni di Teoria Geometrica della Misura e di Calcolo delle Variazioni. Organized by C.I.R.M. and by Mathematics Department, University of Trento, Levico Terme (Trento), Italy. 5/16

6 January 16-20, 2006 Third Trilateral Meeting "Australia-Taiwan-Italia". Workshop INDAM, Mathematics Department, Sapienza, University of Rome, Italy. July 04-08, 2005 Summer School on Calculus of Variations. Memomat Department, Sapienza, University of Rome, Italy. May 29 - June 03, 2005 Infinite Energy Solutions of Partial Differential Equations. Workshop INDAM, Cortona (Arezzo), Italy. March 18-20, 2005 Matematica e Cultura Auditorium Santa Margherita, "Cá Foscari", University of Venice, Italy Memotraining Course. Advanced learning and mnemonic techniques and speed reading, Rome, Italy. INTERNATIONAL CONFERENCES AND COURSES (Organizing committee)... November 12-16, 2012 October 5-6, 2012 October 1-4, 2012 From October 2012 New trends in Nonlinear Parabolic Equations. Organized in collaboration with G. Mingione and G. Palatucci. University of Parma, Italy. Two days on Nonlocal Operators and Applications. Organized in collaboration with G. Palatucci. University of Parma, Italy. Topics in Calculus of Variations and Applications. Organized in collaboration with M. Morini and G. Palatucci. University of Parma, Italy. Other experiences as organizer Organizer of research talks Seminario di Analisi Matematica, In collaboration with L. Angiuli and G. Palatucci. Dipartimento di Matematica e Informatica, University of Parma, Italy. 6/16

7 GIVEN TALKS February 21, 2013 Fractional regularity for nonlinear problems with measure data. Winter School on Fast and Anomalous Diffusion, Sapienza, University of Rome, Italy. December 12, 2012 Measure data problems, lower order terms and interpolation effects. Norwegian-Italian Workshop in PDE s, NTNU, Trondheim, Norway. May 31, 2012 On the Aleksandrov-Bakelman-Pucci estimate for the infinity Laplacian. Workshop on Nonlinear Partial Differential Equations on the occasion of the sixtieth birthday of Patrizia Pucci, Perugia, Italy. May 10, 2012 Measure data problems, lower order terms and interpolation effects. Young Women in PDEs, Institute for Applied Mathematics, Bonn, Germany. November 23, 2011 On the Aleksandrov-Bakelman-Pucci estimate for the infinity Laplacian. Mathematics Department, University of Parma, Parma, Italy. Novembre 10, 2011 On the Aleksandrov-Bakelman-Pucci estimate for the infinity Laplacian. University of Aveiro, Aveiro, Portugal. June 29, 2011 Limits of anisotropic and degenerate elliptic problems. Ninth "Jornades d introducció als sistemes dinàmics i a les EDP s" (JISD 2011), UPC, Barcelona, Spain. May 20, 2011 Limits of anisotropic and degenerate elliptic problems. Second Workshop in Matematical Analysis in Alicante, Alicante, Spain. April 1, 2011 Nonlinear eigenvalues for anisotropic quasilinear degenerate elliptic equations. UT, University of Texas, Austin, Texas, USA. 7/16

8 March 9, 2011 Nonlinear elliptic problems for a class of anisotropic operators. FCT UNL, Faculdade de Ciencia e Tecnologia, Universidade nova de Lisboa, Portugal. December 11, 2009 Nonlinear elliptic problems for a class of anisotropic operators. CMUC, Centre for Mathematics, University of Coimbra, Portugal. February 10, 2009 A semilinear elliptic problem for some anisotropic operators. XIX Convegno Nazionale di Calcolo delle Variazioni, Levico Terme (Trento), Italy. January 23, 2009 Elliptic problems for some anisotropic operators. Workshop on calculus of variations and PDE s, Florence, Italy. November 13, 2008 Alcuni problemi ellittici associati ad un operatore anisotropo, (Some elliptic problems for an anisotropic operator). Mathematics Department, Sapienza, University of Rome, Italy. February 15, 2008 Nonlinear eigenvalues for anisotropic quasilinear degenerate elliptic equations. CMUC, Centre for Mathematics, University of Coimbra, Portugal. July 25, 2007 Existence results of positive solutions of an anisotropic quasilinear elliptic equation. CIM/UC Summer School: "Topics in Nonlinear PDE s", Coimbra, Portugal. VISITING POSITIONS AT MATHEMATICS DE- PARTMENTS AND RESEARCH CENTERS March 27-April 9, 2011 UT Austin Portugal program in Mathematics. Mathematics Department of the University of Texas, Austin, USA. February 13-21, 2008 Prof. Josè Miguel Urbano s invitation. Centro Internacional de Matematica, Coimbra, Portugal. 8/16

9 PUBLICATIONS 1. A. Di Castro, G. Palatucci, Anisotropic De Giorgi classes and Harnack type inequality for certain anisotropic Sobolev spaces, submitted. Abstract. We propose a natural extension of the usual definition of the De Giorgi classes for functions in the anisotropic Sobolev spaces. We investigate the relation of the functions in such classes with the weak solutions to some anisotropic elliptic equations in divergence form as well as with the mini- mizers of the corresponding functionals with anisotropic polynomial growth. As an application, we prove an Harnack type inequality for certain anisotropic Sobolev spaces, in turn implying a strong maximum principle. 2. P. Baroni, A. Di Castro, G. Palatucci, Global estimates for nonlinear parabolic equations, to appear in J. Evol. Equations. Abstract. We consider nonlinear parabolic equations of the type u t div a(x, t, Du) = f(x, t) on Ω T := Ω ( T, 0), under standard growth conditions on a, with f only assumed to be integrable. We prove general decay estimates up to the boundary for level sets of the solutions u and the gradient Du which imply very general estimates in Lebesgue and Lorentz spaces. Assuming only that the involved domains satisfy a mild exterior capacity density condition, we provide global regularity results. 3. A. Di Castro, G. Palatucci, Fractional regularity for nonlinear elliptic problems with measure data, J. Convex. Anal., 20 (2013), No. 3. Abstract. We consider nonlinear elliptic equations of the type div a(x, Du) = µ having a Radon measure on the right-hand side and prove fractional differentiability results of Calderòn-Zygmund type for very weak solutions. We extend some of the results achieved by G. Mingione (2007), in turn improving a regularity result by Cirmi & Leonardi (2010). 9/16

10 4. A. Di Castro, G. Palatucci, Nonlinear parabolic problems with lower order terms and related integral estimates, Nonlinear Anal., 75 (2012), Abstract. We deal with the solutions to nonlinear parabolic equations of the form u t div a(x, t, Du) + g(x, t, u) = f(x, t) on Ω T = Ω ( T, 0) under standard growth conditions on g and a, with f only assumed to be integrable to the power γ > 1. We prove general local decay estimates for level sets of the solutions u and the gradient Du which imply very general estimates in rearrangement function spaces (Lebesgue, Orlicz, Lorentz) and non-rearrangement ones, up to Lorentz-Morrey spaces. 5. A. Di Castro, G. Palatucci, Measure data problems, lower order terms and interpolation effects, to appear in Ann. Mat. Pura Appl. DOI: /s Abstract. We deal with the solutions to nonlinear elliptic equations of the form div a(x, Du) + g(x, u) = f, with f being just a summable function, under standard growth conditions on g and a. We prove general local decay estimates for level sets of the gradient of solutions in turn implying very general estimates in rearrangement and non-rearrangement function spaces, up to Lorentz-Morrey spaces. The results obtained are in clear accordance with the classical Gagliardo-Nirenberg interpolation theory. 6. F. Charro, G. De Philippis, A. Di Castro, D. Maximo, On the Aleksandrov-Bakelman-Pucci estimate for the infinity Laplacian, to appear in Calc. Var. and Partial Differential Equations, available also at arxiv: v1. Abstract. We prove, L bounds and estimates of the modulus of continuity of solutions to the Poisson problem for the normalized infinity and p-laplacian, namely N p u = f for n < p. We are able to provide a stable family of results depending continuously on the parameter p. We also prove the failure of the classical Aleksandrov-Bakelman-Pucci estimate for the normalized infinity Laplacian and propose alternate estimates. 10/16

11 7. A. Di Castro, M. Pérez-Llanos, J. M. Urbano, Limits of anisotropic and degenerate elliptic problems, Commun. Pure Appl. Anal., 11 (2012), Abstract. This paper analyzes the behavior of solutions for anisotropic problems like N p i 2 = f i=1 x i x i x i u = 0 in Ω on Ω where Ω is a bounded, smooth and convex domain in R N, f C(Ω) a given function, as the exponents (p i > N for all i = 1,..., N) go to infinity. We show that solutions converge uniformly to a function that solves, in the viscosity sense, a certain problem that we identify. The results are presented in two-dimensional setting but can be extended to any dimension. 8. A. Di Castro, Local Hölder continuity of weak solutions for an anisotropic elliptic equation, to appear in NoDEA, Nonlinear Differential Equations Appl. DOI : /s Abstract. We prove, following DiBenedetto s intrinsic scaling method, that the weak solution of problem N p i 2 = f i=1 x i x i x i u = 0 in Ω on Ω is locally Hölder continuos, where f is a bounded given function and p i 2, for any i = 1,..., N. 9. A. Di Castro, Anisotropic elliptic problems with natural growth terms, Manuscripta Math., 135 (2011), Abstract. In this paper we prove existence and regularity of solutions for nonlinear elliptic equations of the type N p i 2 + g(x, u, u) = f i=1 x i x i x i in a bounded, smooth, domain Ω in R N, with homogeneous Dirichlet boundary conditions. The right hand side f is assumed to belong to some Lebesgue space and the function g is a nonlinear lower order term. 11/16

12 10. A. Di Castro, E. Montefusco, Nonlinear eigenvalues for anisotropic quasilinear degenerate elliptic equations, Nonlinear Anal., 70 (2009), Abstract. We study the questions of existence, nonexistence and multiplicity of positive solutions for the following class of anisotropic quasilinear elliptic problems N p i 2 = λ u q 2 u i=1 x i x i x i u = 0 in Ω on Ω where Ω is a bounded subset of R N, N 3 and λ > 0 is a real parameter. In particular we are interested to the case p min = min {p i} < q < p max = max {p i}. i=1,...,n i=1,...,n 11. A. Di Castro, Existence and Regularity Results for Anisotropic Elliptic Problems, Adv. Nonlin. Stud., 9 (2009), Abstract. In this paper we deal with existence and regularity of the solutions for the following anisotropic elliptic problem with homogeneous Dirichlet boundary conditions in bounded domains: N p i 2 = f in Ω, i=1 x i x i x i u = 0 on Ω, where the datum f belongs to a Marcinkiewicz space or to a Lebesgue space. We complete the framework of regularity, covering all the possible data f and showing how the regularity of f influences that of solutions. 11 bis. A. Di Castro, Corrigendum to Existence and Regularity Results for Anisotropic Elliptic Problems, Adv. Nonlin. Stud., 9 (2009), A. Di Castro, Elliptic problems for some anisotropic operators, Ph. D. Thesis. Abstract. I present some existence, nonexistence and regularity results for the solutions to some nonlinear elliptic problems in bounded domains of R N with homogeneous Dirichlet boundary conditions associated to a class of anisotropic operators. 12/16

13 RESEARCH INTERESTS Nonlinear elliptic and parabolic problems 1. Existence and regularity results for nonlinear elliptic equations in bounded domain, associated to a class of non-standard growth operators, with Dirichlet boundary conditions. 2. Existence and regularity results for anisotropic elliptic problems with lower order terms. 3. Existence, nonexistence and multiplicity results for degenerate, semilinear, anisotropic elliptic problems. 4. Limits of anisotropic and degenerate elliptic problems. 5. Regularity issues and limiting processes for some PDEs. 6. Fine regularity properties of solutions to nonlinear elliptic and parabolic problems. 7. Calderón-Zygmund type estimates, in particular for measure data problems. MEMBERSHIPS AND GRANTS May 2012 GNAMPA, Gruppo Nazionale di Analisi Matematica, Probabilità e Applicazioni. Grant for the project Metodi variazionali per lo studio di equazioni ellittiche non-locali con operatori di tipo laplaciano frazionario in collaboration with G. Palatucci (University of Parma) and R. Servadei (University of Calabria). From June 2011 Degenerate elliptic and parabolic equations and its applications to front propagation UTA_CMU MAT FCT, Fondação para a Ciência e a Tecnologia (Principal Investigator: Prof. Diogo Gomes, IST, Lisbon, Portugal). From March 2011 Analysis of Nonlinear Partial Differential Equations UTAustin MAT FCT, Fondação para a Ciência e a Tecnologia (Principal Investigator: Prof. José Miguel Urbano, UC, Universidade de Coimbra, Coimbra, Portugal). 13/16

14 From 2005 GNAMPA, Gruppo Nazionale di Analisi Matematica, Probabilità e Applicazioni. (Director: Prof. Italo Capuzzo Dolcetta, Sapienza, University of Rome, Italy). From 2004 Gruppo di Equazioni Differenziali Nonlineari. Sapienza, University of Rome, Italy (Responsable member: Prof. Lucio Boccardo, Sapienza, University of Rome, Italy). PEER REVIEW ACTIVITY Critical reviewer for: 1. Electronic Journal of Differential Equations (from July 2011). 2. Nonlinear Analysis: Theory, Methods & Applications (from November 2011). 3. Mathematical Inequalities & Applications (from April 2012). 4. Forum Mathematicum (from October 2012). 5. Numerical Functional Analysis and Optimization (from January 2013). LANGUAGES Italian English Portuguese mother tongue intermediate Upper Intermediate course, Oxford Institute of Parma, Italy Individual lessons to improve English language, St. George s Institute High Intermediate Level Certificate UPTER-Università Popolare of Rome. intermediate 14/16

15 COMPUTER SKILLS Operative Systems Windows XP, Mac Applications Suite Microsoft Office, Mathematica, Latex INTERESTS Research Art Sailing and travel Scientific research in Pure and Applied Mathematics, concerning elliptic PDE. Interested to anisotropic problems, with Dirichlet boundary conditions in particular to study the existence and regularity of solutions of some equations associated to a differential operator whose partial derivatives are involved with different powers, the pseudo anisotropic laplacian. Interested in reading and good aptitude to drawing. Keen on sailing (with sailing licence) and on travel to know different cultures and countries. REFEREES Prof. David Arcoya Departamento de Análisis Matemático, Universidad de Granada, Spain darcoya@ugr.es phone Prof. Lucio Boccardo Dipartimento di Matematica, Sapienza, Università di Roma, Italy boccardo@mat.uniroma1.it phone Prof. Giuseppe Mingione Dipartimento di Matematica e Informatica, Università degli Studi di Parma, Italy giuseppe.mingione@math.unipr.it phone /16

16 Prof. Maria Michaela Porzio Dipartimento di Matematica, Sapienza, Università di Roma, Italy phone Prof. José Miguel Urbano Departamento de Matemática, Universidade de Coimbra, Portugal phone /16