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Mathematical Analysis group

Group members, publications and research topics

Emilio Acerbi - Publications of 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

Alberto Arosio - Publications of Alberto Arosio
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 - Publications of 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.

Marino Belloni - Publications of 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

Pietro Celada - Publications of Pietro Celada
Calculus of variations: semicontinuity of integral functionals, existence of minimizers for variational problems without lower semicontinuity and differential inclusions.

Alessandra Coscia - Publications of 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.

Luca Lorenzi - Publications of 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.

Alessandra Lunardi - Publications of Alessandra Lunardi
Elliptic, hypoelliptic and parabolic differential equations. Evolution equations in Banach spaces.Infinite dimensional analysis.

Giuseppe Mingione - Publications of Giuseppe Mingione
Calculus of variations, elliptic and parabolic PDE

Massimiliano Morini - Publications of 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

Domenico Mucci - Publications of Domenico Mucci
Calculus of Variations and Geometric Measure Theory

Giampiero Palatucci - Publications of 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.

Stefano Panizzi - Publications of 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. 

Alessandro Zaccagnini - Publications of 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.

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Visiting members

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Main collaborators

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Research projects
  • VECTORIAL PROBLEMS Vectorial Elliptic, Parabolic and Variational Problems: Singularities and Regularity, FP7-IDEAS-ERC Starting Grant, Principal Investigator: Giuseppe Mingione (Cordis)

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Seminars

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Pubblicato Mercoledì, 25 Giugno, 2014 - 12:09 | ultima modifica Venerdì, 27 Ottobre, 2017 - 13:58