Mathematical Analysis group
Emilio Acerbi List of publications - Scopus author profile - Publons profile
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
Alberto Arosio List of publications - Scopus author profile
Initial-boundary value problem for hyperbolic equations: mainly those coming out from solid mechanics, as:
1) Kirchhoff nonlinear vibrating string 1876 (Arosio & Panizzi, Trans. Amer. Math. Soc. 348, No.1 (1996), 305-330 [MR1333386] [Zbl 858:35083]
2) Linear Timoshenko beam (1921)
3) Nonlinear Timoshenko-Kirchhoff beam (Arosio, Chinese Ann. Math. Ser.B, 20, No.4 (1999), p. 495-506) [MR1752752] [Zbl 970.74036]
Paolo Baroni List of publications - Scopus author profile
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.
Marino Belloni List of publications - Scopus author profile
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
Pietro Celada List of publications - Scopus author profile
Calculus of variations: semicontinuity of integral functionals, existence of minimizers for variational problems without lower semicontinuity and differential inclusions.
Alessandra Coscia List of publications - Scopus author profile - Publons profile
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.
Luca Lorenzi List of publications - Scopus author profile
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.
Massimiliano Morini List of publications - Scopus author profile
- nonlocal geometric flows
- free-discontinuity problems: regularity, minimality conditions, variational approximation
- quasistatic evolution in plasticity problems
- variational image processing
- quasilinear elliptic equations in phase transitions problems
Giampiero Palatucci List of publications - Scopus author profile - Publons profile
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.
Stefano Panizzi List of publications - Scopus author profile
- 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.
Alessandro Zaccagnini List of publications - Scopus author profile
- 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.
- 2nd Day for Number Theory Ph.D Students, Parma 12 aprile 2018
- Workshop: Recent advances in Calculus of Variations and PDEs, Parma 15 marzo 2018
- Workshop: Deterministic and stochastic evolution equations, Parma 4,5,6 September 2017
- Workshop: Partial Differential Equations and Applications, Bologna, 22-26 May 2017
- Workshop on Calculus of Variations and its Applications, Parma April 14, 2016
- Sixth Trilateral Meeting on Nonlinear Partial Differential Equations and Applications, Parma December 14-18, 2015
- Workshop on New advances in PDE's, Inverse Problems and Control Theory, Parma July 6-10, 2015