Mathematical Analysis, Probability and Statistics
Emilio ACERBI
Calculus of variations and especially:
- the aspects concerning the mechanics of elastic solids and recently fluids
- some cases of energies possessing a bulk and a surface part, with links to image reconstruction and micromagnetic materials
IRIS - Scopus - WOS
Paolo BARONI
Regularity for elliptic and parabolic PDEs, in particular of p-Laplacian type: Calderón-Zygmund estimates, Linear & nonlinear potentials.
Adams theorems & fine differentiability properties for measure data problems, mainly of parabolic type: DiBenedetto intrinsic geometry approach.
Regularity estimates for (possibly degenerate) phase transition problems. Hölder estimates & Harnack inequalities.
IRIS - Scopus
Marino BELLONI
Calculus of Variations, and more specifically
- Variational problems not convex and not coercive (Newton's Problem of minimal resistance)
- The Lavrentiev phenomenon
- Regularity and simplicity of the first eigenvalue of the infinity Laplacian operator
- Shape optimization problems in the class of convex domains
IRIS - Scopus
Filippo CAGNETTI
Calculus of variations.
IRIS - Scopus
Pietro CELADA
Calculus of variations: semicontinuity of integral functionals, existence of minimizers for variational problems without lower semicontinuity and differential inclusions.
IRIS - Scopus
Alessandra COSCIA
For several years her research focused on the Calculus of Variations, studying in particular functions of Bounded Variation, existence problems, image reconstruction and problems in fracture mechanics.
Presently she is conducting a research of medical interest, in partnership with the Allergological Department of the children section of the Parma Hospital and with several hospitals in the region Emilia Romagna, in charge of data management and mathematical-informatic-statistical treatment of data.
In particular these researches address children allergies, diabetes and respiratory diseases.
IRIS - Scopus - WOS
Cristiana DE FILIPPIS
Calculus of variations.
IRIS - Scopus
Luca LORENZI
Degenerate and nondegenerate elliptic and parabolic operators with unbounded coefficients in unbounded domains;
Reaction-diffusion systems and Free boundary problems with particular attention to the stability analysis.
IRIS - Scopus
Giuseppe MINGIONE
Calculus of variations, elliptic and parabolic PDE
IRIS - Scopus - WOS
Francesco MORANDIN
Dyadic shell models in fluid mechanics. In particular, anomalous dissipation for nonlinear models (both deterministic and stochastic) derived from the 3-dimensional Euler and Navier-Stokes equations.
Urn processes. In particular, large deviations principles in generalized urn models.
Branchig processes. In particular applied to the construction of explicit solutions of nonlinear ODE's.
Statistical mechanics. In particular, spin glass models related to error correcting codes: random energy model, random codes, LDPC codes, turbocodes.
Massimiliano MORINI
- nonlocal geometric flows
- free-discontinuity problems: regularity, minimality conditions, variational approximation
- quasistatic evolution in plasticity problems
- Gamma-convergence
- variational image processing
- quasilinear elliptic equations in phase transitions problems
IRIS - Scopus
Domenico MUCCI
Calculus of Variations and Geometric Measure Theory
IRIS - Scopus - WOS
Giampiero PALATUCCI
Calculus of Variations and PDE
Keywords: Phase transitions, Concentration, Homogenization, critical Sobolev embeddings, Nonlocal singular perturbations, Fractional operators, Dislocations, Gamma-convergence, Minimal surfaces, Measure data, Regularity in non-rearrangement spaces, Calderón-Zygmund, Yamabe problem, Obstacle problem.
IRIS - Scopus - WOS
Stefano PANIZZI
- Hyperbolic equations: local/global in time solvability of nonlinear hyperbolic equations (Kirchhoff -string equation); well-posedness of the mixed problem for higher order linear/nonlinear equations in bounded domains; unilateral problems; propagation of regularity for semilinear wave equations.
- Wave scattering: variational formulations of time-domain boundary integral equations.
- Nonlinear ODEs: stability of periodic solutions.
IRIS - Scopus
Alessandro ZACCAGNINI
- Distribution of prime numbers (also in short intervals or arithmetic progressions) and additive problems similar to Goldbach's.
- Some properties of the Riemann zeta-function.
IRIS - Scopus
Paolo DE FAZIO
Ciclo XXXVI. Advisor: A. Lunardi
Mirco PICCININI
Ciclo XXXVI. Advisor: G. Palatucci
PRIN 2022 - Geometric Evolution Problems and Shape Optimization (GEPSO) (2022E9CF89)
Coordinatore Nazionale: N. Fusco (Università di Napoli Federico II). Coordinatore Locale Unità di Parma: M. Morini.
PRIN PNRR - Magnetic skyrmions, skyrmionic bubbles and domain walls for spintronic applications (P2022WJW9H)
Coordinatore Nazionale: C. Muratov (Università di Pisa). Coordinatore Locale Unità di Parma: M. Morini.