Francesco Esposito's Homepage - Research interests

Curriculum Vitae

Full CV in English here.

Research Interests

Keywords: Partial Differential Equations; Semilinear Elliptic Equations; Quasilinear Elliptic Equations; Qualitative properties of the solutions; Regularity of the solutions; Existence of solutions; Moving plane method; Geometric and qualitative properties of solutions;

Preprints and Publications

S. BIAGI, F. ESPOSITO, L. MONTORO AND E. VECCHI. On mixed local-nonlocal problems with Hardy potential. Submitted, 2024. Arxiv
S. BIAGI, F. ESPOSITO, A. RONCORONI AND E. VECCHI. Brezis-Nirenberg-type results for the anisotropic p-Laplacian. Submitted, 2024. Arxiv
F. ESPOSITO, R. LÓPEZ-SORIANO AND B. SCIUNZI. Classification of solutions to Hardy-Sobolev Doubly Critical Systems. J. Math. Pure Appl., 2024, 189, 103595. Arxiv, Paper
F. ESPOSITO, L. MONTORO, B. SCIUNZI AND D. VUONO. Asymptotic behaviour of solutions to the anisotropic Finsler doubly critical equation. Calc. Var. Partial Differential Equations, 2024, 63(3), Paper no. 77. Arxiv, Paper
F. ESPOSITO, B. SCIUNZI AND N. SOAVE. Notes on Overdetermined Singular Problems. Bull. Lond. Math. Soc., 56(4), pp. 1341–1350. Arxiv, Paper
F. ESPOSITO, B. SCIUNZI AND A. TROMBETTA. Existence and uniqueness for anisotropic quasilinear elliptic equations involving singular nonlinearities. Discrete Contin. Dyn. Syst., 2024, 44(6), pp. 1628–1646. Paper
S. BIAGI, F. ESPOSITO, L. MONTORO AND E. VECCHI. Symmetry and monotonicity of singular solutions to p-Laplacian systems involving a first order term. Advances in Calculus of Variations, 2024, 17(4), pp. 1519-1541. Arxiv, Paper
F. ESPOSITO, G. RIEY, B. SCIUNZI AND D. VUONO. Anisotropic Kelvin-type transform for a class of anisotropic elliptic operators. Diff. Int. Eq. 36(7-8), 2023, pp. 715-726. Arxiv, Paper
F. ESPOSITO AND A. TROMBETTA. Qualitative properties of blow-up solutions to some semilinear elliptic systems in non-convex domains. Nonlin. Anal RWA, 71, 2023, 103804. Paper
S. BIAGI, F. ESPOSITO AND E. VECCHI. Symmetry of intrinsically singular solutions of double phase problems. Diff. Int. Eq. 36(3-4), 2023, pp. 229–246. Arxiv, Paper
F. ESPOSITO, B. SCIUNZI AND A. TROMBETTA. Regularity and symmetry results for nonlinear degenerate elliptic equations. J. of Differential Equations, 336, 2022, pp. 315–333. Arxiv, Paper
F. ESPOSITO, A. FARINA, L. MONTORO AND B. SCIUNZI. Monotonicity of positive solutions to quasilinear elliptic equations in half-spaces with a changing-sign nonlinearity. Calc. Var. Partial Differential Equations, 61(4), 2022, Paper no. 154. Arxiv, Paper
F. ESPOSITO, A. FARINA, L. MONTORO AND B. SCIUNZI. On the Gibbons' conjecture for equations involving the p-Laplacian. Math. Ann., 382(1-2), 2022, pp. 943-974. Arxiv, Paper
F. ESPOSITO AND B. SCIUNZI. The moving plane method for doubly singular elliptic equations involving a first order term. Adv. Nonlinear Stud., 21(4), 2021, pp. 905-916. Arxiv, Paper
S. BIAGI, F. ESPOSITO AND E. VECCHI. Symmetry and monotonicity of singular solutions of double phase problems. J. of Differential Equations , 280, 2021, pp. 435-463. Arxiv, Paper
F. ESPOSITO, S. MERCHAN AND L. MONTORO. Symmetry results for p-Laplacian systems involving a first order term. Ann. Mat. Pura Appl. (4) 200 (2021), no. 5, pp. 2313–2331. Arxiv, Paper
F. ESPOSITO AND B. SCIUNZI. On the Hopf boundary lemma for quasilinear problems involving singular nonlinearities and applications. J. Funct. Anal. 278(4), 2020, 108346. Arxiv, Paper
F. ESPOSITO. Symmetry and monotonicity properties of singular solutions to some cooperative semilinear elliptic systems involving critical nonlinearity. Discrete Contin. Dyn. Syst., 40(1), 2020, pp. 549–577. Arxiv, Paper
A. CANINO, F. ESPOSITO AND B. SCIUNZI. On the Hopf boundary lemma for singular semilinear elliptic equations. J. of Differential Equations 266(9), 2019, pp. 5488–5499. Paper
F. ESPOSITO, L. MONTORO AND B. SCIUNZI. Monotonicity and symmetry of singular solutions to quasilinear problems. J. Math. Pure Appl. 126, 2019, pp. 214–231. Arxiv, Paper
F. ESPOSITO, A. FARINA AND B. SCIUNZI. Qualitative properties of singular solutions to semilinear elliptic problems. J. of Differential Equations. 265(5), 2018, pp. 1962–1983. Arxiv, Paper

Invited Talks & Seminars

Rigidity and symmetry results of some elliptic problems in punctured domains, Seminario de Ecuaciones Diferenciales, organized by Rafael López Soriano and David Poyato, Universidad de Granada, Granada (20 March 2025).
Symmetry results for Hardy-Sobolev nonlinear critical systems, Recent progress in PDEs, organized by Riccardo Durastanti, Francescantonio Oliva, Francesco Petitta at University of Rome "Sapienza", Rome (19-20 February 2025).
Symmetry and rigidity results for nonlinear elliptic problems in bounded domains, Seminario di Analisi Matematica, Dipartimento di Analisi Matematica e Applicazioni "R. Caccioppoli", organized by Daniel Castorina at University of Naples "Federico II" (22 January 2025).
On the classification of solutions for Hardy-Sobolev doubly critical systems - Session: Recent advances in systems of PDEs organized by Ángel Arroyo García, Rafael López Soriano, Alejandro Ortega García during XXVIII Congreso de ecuaciones diferenciales y aplicaciones / XXVIIIcongreso de matemática aplicada (cedya/cma) at University of Bilbao, Bilbao (24-28 June 2024).
Rigidity and symmetry results for some elliptic problems, NonPUB 2024 organized by Nicola Abatangelo, Berardo Ruffini, Eugenio Vecchi at University of Bologna - Alma Mater Studiorum, Bologna (6-7 June 2024).
Symmetry Results for Elliptic PDEs, DeMaCS Seminar Series. University of Calabria, Rende (30 May 2024).
Overdetermined Singular Problems, International Conference on Elliptic and Parabolic Problems: GAETA 2024. Gaeta (20-24 May 2024).
Classification of solutions for some semilinear doubly critical elliptic systems - Seminario de Ecuaciones Diferenciales organized by Rafael López Soriano and David Ruiz, Universidad de Granada, Granada (25 April 2024).
Classification of solutions for a Gross-Pitaevskii type system - Calculus of Variations and Free Boundary Problems VIII organized by Roberto Ognibene, Giorgio Tortone and Bozhidar Velichkov, University of Pisa, Pisa (11-12 April 2024).
Classification of solutions to Hardy-Sobolev doubly critical systems, Atlantic Conference in Nonlinear PDEs - Dispersive and Elliptic Equations and Systems organized by Simão Correia, James Kennedy, Hugo Tavares, Gianmaria Verzini at Instituto Superior Técnico - Universidade de Lisboa, Lisbon (30 October - 3 November 2023).
A classification result for Hardy-Sobolev semilinear elliptic system, Recent advances in nonlinear partial differential equations organized by Stefano Buccheri, Rita Cirmi, Salvatore D'Asero, Salvatore Leonardi and Maria Michaela Porzio at University of Catania, Catania (24-26 May 2023).
A classification result for a Gross-Pitaevskii type system, Seminario di Analisi Matematica organized by Stefano Biagi and Matteo Muratori at Politecnico di Milano, Milano (13 April 2023).
Symmetry results via the moving planes method; Mathematical Analysis seminars organized by Joshua Kortum and Francesco De Anna at University of Wuerzburg, Zoom (1 December 2022).
Symmetry results for singular solutions to the p-Laplace equation; Seminario di Equazioni Differenziali organized by Riccardo Molle and Gabriella Tarantello at University of Rome "Tor Vergata, Rome (29 November 2022).
The moving plane technique for singular solutions to elliptic problems; Seminario di Analisi Matematica organized by Benedetta Pellacci at University of Campania"Luigi Vanvitelli", Caserta (21 November 2022).
An Hopf-type lemma for elliptic problems involving singular nonlinearities; International E-Conference on Mathematical and Statistical Science organized by Tuncer Acar at Selçuk University, Turkey (22 October 2022).
Quasilinear elliptic problems with sign-changing nonlinearities; P(n)/N(p) : Problemi differenziali nonlineari/Nonlinear differential problems organized by Giulio Galise, Fabiana Leoni, Filomena Pacella, Benedetta Pellacci at University of Rome "Sapienza", Roma (20 October 2022).
Monotonicity of positive solutions to quasilinear elliptic equations in half-spaces with a changing-sign nonlinearity; Horizons in nonlinear PDEs organized by Anna Dall'Acqua, Emil Wiedemann, Rico Zacher at University of Ulm, Ulm (26-30 September 2022). Talk, Poster
A symmetry result for an elliptic system with doubly critical growth; Qualitative and quantitative aspects of non-linear PDEs organized by Anna Maria Candela, Francesco Chiacchio, Silvia Cingolani, Giulio Ciraolo, Pietro d’Avenia, Francesca Dalbono, Berardino Sciunzi, Giusi Vaira at Università degli studi di Bari "Aldo Moro", Bari (5-9 September 2022).
Gibbons’ conjectures for the Allen-Cahn equation - Special Session: Methods of functional analysis in approximation problems, differential equations and integral equations, organized by Luigi Muglia and Vittorio Colao during the Conference: Functional Analysis, Approximation Theory and Numerical Analysis, Matera (5-8 July 2022).
The moving planes method for some singular semilinear and quasilinear elliptic problems, seminar as invited speaker organized by Eduardo Colorado and Rafael Lòpez Soriano at Universidad Carlos III de Madrid (3 May 2022).
The Hopf boundary lemma for singular elliptic problems, XMaths Workshop 2021 organized by Alessandro Camasta, Dario Di Pinto, Marco Gallo, Marilena Ligabò, Nicola Picoco, Laura Selicato, Caterina Sportelli and Cristiano Tamborrino at Università degli studi di Bari "Aldo Moro", Bari (21-22 December 2021).
Quasilinear version of the Gibbons’ conjecture, Recent Advances in Analysis, PDEs and Applications organized by Giulia Meglioli, Matteo Muratori, Clara Patriarca and Fabio Punzo at Politecnico di Milano, Milano (2-3 December 2021).
Some adaptations of the moving planes method to singular elliptic problems, Seminario di Analisi Matematica organized by Nicola Soave and Matteo Muratori at Politecnico di Milano, Milano (9 June 2021).
The moving planes method of Aleksandrov-Serrin for some semilinear elliptic problems, Young Researchers Colloquium, organized by Jacek Krajczok, Filip Rupniewski and Jacopo Schino on Zoom, Institute of Mathematics Polish Academy Sciences of Warsaw (23 October 2020).
Symmetry and Monotonicity Properties of Singular Solutions to some Semilinear and Quasilinear Elliptic Problems, Minisimposya: Singular and degenerate PDEs, organized by Francescantonio Oliva and Francesco Petitta during the International Conference on Elliptic and Parabolic Problems, Gaeta (20-24 May 2019).
On the Moving Plane Method for Singular Solutions to some Semilinear and Quasilinear Elliptic Problems, Workshop during Lectures in Nonlinear Analysis and Differential Equations organized by Gennaro Infante, Cosenza (8-12 April 2019).
Qualitative Properties of Singular Solutions to some Semilinear and Quasilinear Elliptic Problems, Séminaire d'Analyse Appliquée organized by Jean-Paul Chehab, Alberto Farina, Olivier Goubet, LAMFA Université de Picardie Jules Verne, Amiens (9 April 2018).

Organization of Conferences

Analysis and PDEs, organized by Francesco Esposito, Luigi Montoro. University of Calabria, Rende (18 November 2021). Poster
Proprietà qualitative per soluzioni di equazioni ellittiche non-lineari, organized by Francesco Esposito, Luigi Montoro, Berardino Sciunzi and Alessandro Trombetta at University of Calabria. Rende (27-28 April 2022). Poster, Website
Elliptic and Parabolic PDEs and Applications, organized by Francesco Esposito, Giuseppe Riey, Berardino Sciunzi and Domenico Vuono at University of Calabria. Rende (20-21 April 2023). Website
Nonlinear PDEs in Cosenza, organized by Fabio Ciolli, Francesco Esposito, Felice Iandoli, Luigi Montoro, Luigi Muglia, Berardino Sciunzi and Alessandro Trombetta at Cosenza annd at University of Calabria. Cosenza-Rende (16-19 May 2023). Website
Singular, degenerate and anisotropic PDEs, organized by, Francesco Esposito and Giuseppe Riey at Gaeta during the International Conference on Elliptic and Parabolic Problems: GAETA 2024. Gaeta (20-24 May 2024). Website
A summer school on regularity theory in the south of Italy, organized by \textbf{Francesco Esposito, Felice Iandoli, Luigi Montoro, Luigi Muglia, Berardino Sciunzi and Alessandro Trombetta} at University of Calabria, Rende (8-12 July 2024). Website

PhD Courses

Regularity of weak solutions to −∆u =f, organized by PhD Programme in Mathematics and Computer Science of University of Calabria, 12h, Rende (27 September 2021 - 1 October 2021). Poster
Topics in PDEs organized by PhD Programme in Mathematics and Computer Science of University of Calabria, 12h, Rende (March 2024).

Projects

Principal Investigator of GNAMPA-INDAM PROJECT 2025: Problemi singolari e degeneri: esistenza, unicità e analisi delle proprietà qualitative delle soluzioni, Members: Rosa Barbato, Stefano Biagi, Francesco Della Pietra, Riccardo Durastanti, Francescantonio Oliva, Giuseppe Riey, Eugenio Vecchi.
Member of GNAMPA-INDAM PROJECT 2024: Esistenza, unicità e regolarità di soluzioni per problemi singolari, P.I. Francescantonio Oliva. Members: Francesco Della Pietra, Francesco Esposito, Giuseppe Riey, Eugenio Vecchi.
Member of GNAMPA-INDAM PROJECT 2023: Variational and non-variational problems with lack of compactness, P.I. Luigi Montoro. Members: Francesco Esposito, Gianmarco Giovannardi, Luigi Muglia, Dimitri Mugnai, Edoardo Proietti Lippi, Berardino Sciunzi, Eugenio Vecchi.
Member of PRIN PROJECT PNRR 2022: Linear and Nonlinear PDE’s: New directions and Applications, P.I. Cristina Trombetti. Members: Vincenzo Amato, Rossella Bartolo, Anna Maria Candela, Erasmo Caponio, Raffaele Carlone, Francesco Chiacchio, Silvia Cingolani, Pietro D'Avenia, Francesco Della Pietra, Francesco Esposito, Vincenzo Ferone, Marco Gallo, Felice Iandoli, Nunzia Gavitone, Gabriel Mancini, Alba Lia Masiello, Antonio Masiello, Anna Mercaldo, Federica Menunni, Luigi Montoro, Luigi Muglia, Alessio Pomponio, Giuseppe Riey, Addolorata Salvatore, Berardino Sciunzi, Caterina Sportelli, Giusi Vaira, Giuseppina Vannella, Domenico Vuono.
Member of GNAMPA-INDAM PROJECT 2022: PDE ellittiche a diffusione mista, P.I. Nicola Abatangelo. Members: Stefano Biagi, Francesco Esposito, Luigi Montoro, Dimitri Mugnai, Edoardo Proietti Lippi, Eugenio Vecchi, Domenico Vuono.
Principal Investigator of the GNAMPA-INDAM RESEARCH UNIT PROJECT 2022: Proprietà Qualitative per Soluzioni di Equazioni Ellittiche Non-Lineari. Members: Luigi Montoro, Berardino Sciunzi.
Member of the ICTP-INdAM "Research in Pairs" Programme 2020. P.I. Mousoumi Bhakta. Members: Anup Biswas, Luigi Montoro, Francesco Esposito.
Member of PRIN PROJECT 2017: Qualitative and quantitative aspects of nonlinear PDEs, P.I. Berardino Sciunzi. Members: Anna Maria Candela, Giulio Ciraolo, Francesco Chiacchio, Pietro D’Avenia, Francesco Esposito, Isabella Ianni, Luigi Montoro, Benedetta Pellacci, Alessio Pomponio, Giuseppe Riey, Giusi Vaira.
Member of PICS PROJECT 2018: Valeurs propres d’un opérateur Aharonov-Bohm avec pôle variable, P.I. Benedetta Noris. Members: Laura Abatangelo, Luc Hillairet, Francesco Esposito, Alberto Farina, Veronica Felli, Roberto Ognibene.
Member of GNAMPA-INDAM PROJECT 2018: Problemi ellittici semilineari: Alcune idee variazionali, P.I. Anna Maria Candela. Members: Sara Barile, Annnamaria Canino, Francesco Esposito, Addolorata Salvatore.
Member of GNAMPA-INDAM PROJECT 2017: Proprietà qualitative per soluzioni di equazioni ellittiche e paraboliche locali e non-locali, P.I. Berardino Sciunzi. Members: Annamaria Canino, Francesco Esposito, Luigi Montoro.

Page updated

Google Sites

Report abuse