Seminario di Calcolo delle Variazioni & Equazioni alle Derivate Parziali

I seminari si tengono di norma di venerdì alle ore 14:30 nella Sala Conferenze "Franco Tricerri" del Dipartimento di Matematica e Informatica "Ulisse Dini" (Viale Morgagni 67/A).
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A.A. 2018 / 2019


16 novembre


Lubos Pick (Charles Univ)
Higher-order Sobolev embeedings, isoperimetric problem and Frostman measures

Abstract: We will survey both classical and modern techniques and results on higher-order Sobolev embeddings and trace embeddings. We shall focus on sharpness of function spaces in such embeddings obtained via reduction principles.

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23 novembre


Frank Duzaar (U. Erlangen)

30 novembre


Riccardo Adami (PoliTo)
The problem of the Ground States for the Nonlinear Schroedinger Equation on Metric Graphs: the two-dimensional grid

Abstract: Motivated by the study of the Ground State of Bose-Einstein Condensate on complicated structures, the problem of minimizing the NLS energy on metric graphs has been recently addressed in a sistematic way, exploring the cases of finite graphs with halflines, periodic graphs and trees. We give results for the two-dimensional grid, both in the Lˆ2 subcritical and critical cases. We show that the interdimensional structure of the grid, gives rise to a phenomenon called dimensional crossover, involving a continuum of Lˆ2-critical nonlinearity. This is a joint project with Simone Dovetta, Enrico Serra, Lorenzo Tentarelli, and Paolo Tilli.
14 dicembre


Simone Di Marino (INdAM, SNS)


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26 ottobre


Marco Barchiesi (Unina)
Stability of the Gaussian Isoperimetric Inequality

Abstract: I will present an analysis of the sets that minimize the gaussian perimeter plus the norm of the barycenter. These two terms are in competition, and in general the solutions are not the half-spaces. In fact we prove that when the volume is close to one, the solutions are the strips centered in the origin. As a corollary, we obtain that the symmetric strip is the solution of the Gaussian isoperimetric problem among symmetric sets when the volume is close to one. Co-Author: Vesa Julin
Lunedì 24 settembre


Jan Kristensen (University of Oxford)
Regularity for minimizers of variational integrals of (1,p) growth

Abstract: In this talk I present some recent results on the partial regularity of BV minimizers for strongly quasiconvex variational integrals. The focus will be on the case of integrands satisfying linear growth conditions, but for the sake of illustrating the flexibility of a key argument, I'll show how it also applies in the (1,p) growth case when p is less than n/(n-1). The results are part of joint work with Franz Gmeineder (Bonn)
19 ottobre


Andrea Marchese (Unipv)
Local minimality of strictly stable extremal submanifolds

Abstract: I will discuss a recent extension of a result by Brian White, who proved that any smooth, compact submanifold, which is a strictly stable critical point for an elliptic parametric functional, is the unique minimizer in its homology class, if the minimization problem is restricted to a certain geodesic tubular neighborhood of the submanifold. We replace the tubular neighborhood with one induced by the flat distance of integral currents and we provide quantitative estimates. The proof is based on the so called "selection principle", which, via a penalization technique, allows us to recast the problem in the class of graphs, exploiting the regularity theory for almost minimizers. Joint work with D. Inauen (Zurich).

Organizzatori: Chiara Bianchini, Matteo Focardi.
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