Members
Research Profile
The research of the Mathematical Analysis group at the Department of Mathematics and Physics of University of Campania “Luigi Vanvitelli” focuses on the study of Dynamical Systems, nonlinear Partial Differential Equations, of issues in Calculus of Variations, and topics in Probability and Statistics, with particular emphasis on problems arising in the context of ecology, economics, elasticity, electromagnetism, electrostatics, ferromagnetism, fluid dynamics, liquid crystals, nonlinear optics, population dynamics, and quantum mechanics. Also, the group is interested in theoretical problems in the fields of Real Analysis and Measure Theory. In particular, the group is interested in studying
- Geometric variational problems with competing energies.
- Hardy-type inequalities, weak inequalities for maximal functions, and Carleman estimates. Isoperimetric inequalities.
- Homogenization and dimensional reduction.
- Qualitative analysis of solutions to PDEs via symmetrization techniques.
- Real dynamics and linear dynamics on Banach spaces: stability, chaos and hyperbolic properties.
- Spectral optimization in elliptic problems.
- Variational methods and concentration phenomena in nonlinear elliptic systems.
- Well-posedness, spectral properties, properties of dispersion, unique continuation and uncertainty principles in PDEs.
- Fractional stochastic processes.
- Statistical analysis of data and development of numerical algorithms for stochastic models.
Keywords
- Dynamical Systems
- Calculus of Variations
- Nonlinear PDEs
- Probability and statistics
- Real Analysis and Measure Theory
ERC Keywords
- PE1_8
- PE1_9
- PE1_10
- PE1_11
- PE1_13
- PE1_14
- PE1_19
- PE1_20
ISI WEB subject categories
Current research projects (2020-24)
International projects
- “Harmonic Analysis and Differential Equations: New Challenges” (ERCEA - Advanced Grants 2014: 669689 –HADE), Coordinator: Luis Vega (Spain).Period: 1/12/2015 30/11/2021.
- Croatian Science Foundation Project “Homogenization, dimension reduction and structural optimization in continuum mechanica”. Coordinator: Prof. Igor Velcic (Zagreb University, Croatia). Period: 5/10/201815/10/2022.
- “Mathematical models for interacting dynamics on networks” (COST Action CA18232) in Workgroup “Variational methods on graphs and networks”. Coordinator: Delio Mugnolo (Germany). Period:4/10/2019 03/10/2023.
- "Partial Differential Equations: reaction-diffusion, integro-differential, and mathematical physics problems" PID2021-123903NB-I00, Ministerio de Ciencia e Innovación, Gobierno de España, 2022. Coordinatore: Prof. Xavier Cabré (ICREA and UPC) and Albert Mas (UPC). Periodo: 2022 2026
- Cassini Senior Program 2023 “Analisi matematica di materiali innovativi / Analyse mathématique de matériaux innovants”. Coordinator: Prof. Antonio Gaudiello (Università degli Studi della Campania Luigi Vanvitelli).
National Projects
- GNAMPA-INdAM Project 2020, “Problemi variazionali in domini a struttura geometrica complessa”. Coordinator: Prof. Valeria Chiadò Piat (Politecnico di Torino)
- GNAMPA-INdAM Project 2020 "Equazioni ellittiche non lineari". Coordinator: Prof. Massimo Grossi (Sapienza Università di Roma).
- GNAMPA-INdAM Project 2020 “Equazioni di tipo dispersivo: teoria e metodi”. Coordinator: Prof. Piero D’Ancona (Sapienza Università di Roma).
- GNAMPA-INdAM Project 2020 “Problemi stazionari ed evolutivi in varie ipotesi di crescita”. Coordinator: Prof. Fernando Farroni (Università degli Studi di Napoli Federico II).
- GNAMPA-INdAM Project 2022 “PDEs regolarità delle soluzioni, disuguaglianze collegate e applicazioni”. Coordinator: Prof. Chiara Leone (Università degli Studi di Napoli Federico II).
- GNAMPA-INdAM Project 2022 "Studi asintotici in problemi parabolici ed ellittici” Coordinator: Prof. Benedetta Noris (Politecnico di Milano).
- GNAMPA-INdAM Project 2022 “Dispersion and stability in incompressible fluid dynamics”. Coordinator: Stefano Scrobogna (Università degli Studi di Trieste).
- GNAMPA-INdAM Project 2023 “Analisi spettrale per equazioni di Dirac e applicazioni”. Coordinator: Prof. William Borrelli (Università Cattolica del Sacro Cuore).
- GNAMPA-INdAM Project 2023 “Metodi varazionali e PDE per problemi anisotropi”. Coordinator: Prof. Giuseppe Riey (Università della Calabria).
- GNAMPA-INdAM Project 2023, “Omogeneizzazione, controllo e problemi inversi”. Coordinator Prof. Umberto De Maio (Università degli Studi di Napoli Federico II).
- GNAMPA-INdAMProject2024 “DYNAMIChE: DYNAmical Methods: Inverse problems, Chaos and Evolution”. Coordinator: Prof. Luca Zampogni (Università di Perugia).
- GNAMPA-INdAMProject2024 "Metodi Variazionali e topologici per alcune equazioni di Schrödinger non lineari". Coordinator: Prof. Vincenzo Ambrosio (Università Poilitecnica delle Marche)
- GNAMPA-INdAMProject2024 “Proprietà dispersive per equazioni di Dirac”. Coordinator: Biagio Cassano (Università degli Studi della Campania Luigi Vanvitelli).
- PRIN 2017 “Stochastic Models For Complex Systems”, Coordinatore: F. Durante (Università degli Studi del Salento). 15-02-2019 15-07-2023.
- PRIN 2022 “Quantitative Approaches for Green Bond Market: Risk Assessment, Agency Problems and Policy Incentives”. (QNT4GREEN), Prot. PRIN-2022JRY7EF, Coordinator: Prof. Davide Radi (Università Cattolica del Sacro Cuore).
- PRIN 2022 “Geometric-Analytic Methods for PDEs and Applications (GAMPA)”. Coordinator: Prof. Elvise Berchio (Politecnico di Torino)
- PRIN 2022 "Pattern formation in nonlinear phenomena". Coordinator: Susanna Terracini (Università degli Studi di Torino).
- PRIN PNRR 2022 “EXPRESS”. Coordinator: Prof. Alberto Petrillo (Università degli Studi di Napoli Federico II).
- PRIN, PNRR “Vibration Energy Harvesters featuring Smart Power Electronic Interfaces towards Resilient IoT (ESPERI)”,Coordinator:Daniele Davino (Università del Sannio).
- PRIN 2022 “Anomalous Phenomena on Regular and Irregular Domains: Approximating Complexity for the Applied Sciences”, Local Coordinator: Enrica Pirozzi (Università degli Studi della Campania Luigi Vanvitelli).
- PRIN-PNRR “Stochastic models in biomathematics and applications”, Local Coordinator: Enrica Pirozzi (Università degli Studi della Campania Luigi Vanvitelli).
- Complex System Maintenance (COSYMA) Project. Coordinator: Prof. Stefano Marrone (Università degli Studi della Campania Luigi Vanvitelli).
Local projects
- Project of Università degli Studi della Campania Luigi Vanvitelli “VArIational methods and Numerical techniques: sHape Optimization and nonlinear Partial differential EquationS” (Vain-Hopes). Coordinator: Prof. Benedetta Pellacci (Università degli Studi della Campania Luigi Vanvitelli). Period: 02/12/20192/1/2023.
- Project of Università degli Studi della Campania Luigi Vanvitelli “Diffusion in non-classical settings: nonlinear, nonlocal, anisotropic and chaotic phenomena” (START). Coordinator: Dott. Biagio Cassano (Università degli Studi della Campania Luigi Vanvitelli).
Some recent publications (2020-23)
- Abundo, E. Pirozzi, Fractionally integrated Gauss-Markov processes and applications, Commun. Nonlinear sci. Numer. Simul. 101(2021), paper n. 105862.
- Alberico, G. di Blasio, F. Feo, An eigenvalue problem for the anisotropic $\Phi$-Laplacian, J. Differential Equations269 (2020), 6, 4853-4883.
- Ascione, E. Pirozzi, B. Toaldo, On the Exit Time from Open Sets of some Semi-Markov Processes, Ann. Appl. Probab.30, (2020), 3, 1130-1163.
- Brock, J.I. Diaz, A. Ferone, D. Gomez-Castro, A. Mercaldo, Steiner symmetrization for anisotropic quasilinear equations via partial discretization, Ann. Inst. H. Poincaré C Anal.Non Linéaire38 (2021), 2, 347–368.
- Cassano, L. Cossetti, L. Fanelli, Improved Hardy-Rellich inequalities, Commun.Pure Appl. Anal.21 (2022), 3, 867-889,
- Cassano, V. Lotoreichik, A. Mas, M. Tušek, General δ-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation, Rev. Mat. Iberoam. (2022).
- Croce, Z. Fattah, G. Pisante, A reverse isoperimetric inequality for (α− β)-convex bodies, ESAIM. COCV28(2022), article n. 62.
- D’Aniello, U.B. Darji, M. Maiuriello,Generalized hyperbolicity and shadowing in Lp spaces, J. Differential Equations 298(2021), 68–94.
- D'Aniello, L. Moonens, J.M. Rosenblatt, Differentiating Orlicz spaces with rare bases of rectangles, Ann. Acad. Sci. Fenn. Math.45(2020), 1, 411-427.
- Della Pietra, G. di Blasio, N. Gavitone, Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle, Adv. Nonlinear Anal.9(2020), 1, 278-291.
- Di Blasio, G. Pisante, G. Psaradakis, A weighted anisotropic Sobolev type inequality and its applications to Hardy inequalities, Mathematische Annalen379(2021), 1343-1362
- Ferone, A. Mercaldo, S. Segura de Leon, A singular elliptic equation and a related functional, ESAIM Control Optim. Calc. Var.27(2021), Paper N. 39.
- Gaudiello, D. Gomez, M.E. Pérez, Asymptotic analysis of the high frequencies for the Laplace operator in a thin T-like shaped structure, J. Math. Pures Appl. (9)134 (2020), 299-327.
- Gaudiello, D. Gomez, M.E. Pérez, A spectral problem for the Laplacian in joined thin films, Calc. Var. Partial Differential Equations, 62, Article number: 129 (2023).
- Maia, B. Pellacci, D. Schiera, Symmetric positive solutions to nonlinear Choquard equations with potentials. Calc. Var. Partial Differential Equations 61(2022),2, Paper n.61, 34 pp.
- Mazzoleni, B. Pellacci, G.Verzini,Asymptotic spherical shapes in some spectral optimization problems, J. Math. Pures Appl. (9) 135 (2020), 256-283.