Mercoledì 12 Novembre 2025, alle ore 15.00, nella sala professori al livello 1, il prof. Yi Zhang dell’Accademia delle Scienze di Pechino terrà un seminario dal titolo

Weak solutions to Serrin’s overdetermined problem

Abstract:

Serrin’s classical overdetermined theorem states that if a bounded C^2-domain supports a function

with a constant Laplacian that satisfies both constant Dirichlet and Neumann boundary conditions,

then the domain must be a ball. In this presentation, we explore this problem further, demonstrating

that the theorem’s conclusion extends to a broader class of domains, including Lipschitz domains.

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SEMINARIO di ANALISI MATEMATICA
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Giovedì 13 Novembre 2025, alle ore 15:00 nell’Aula Professori al I Livello del DMA, il Professor Julio D. Rossi dell’Università di Buenos Aires, terrà il seguente seminario:

Title: The flow by minimal curvature.

Abstract; in this talk we look for the convex hull of a set using the geometric evolution by minimal curvature of a hypersurface that surrounds the set. To find the convex hull, we study the large time behavior of solutions to an obstacle problem for the level set formulation of the geometric flow driven by the minimum of the principal curvatures (that coincides with the mean curvature flow only in two dimensions). We prove that the superlevel set where the solution to this obstacle problem is positive converges as time goes to infinity to the convex hull of the obstacle. Our approach is based on a game-theoretic approximation for this geometric flow that is inspired by previous results for the mean curvature flow.

Giammichele Di Matteo (SSM Napoli) – Seminario di Analisi

Martedì, 25 novembre⋅15:00 – 16:00

Title: Higher dimensional Sacks-Uhlenbeck approximation

Abstract: In this talk, we will describe a generalization of Sacks-Uhlenbeck’s existence of harmonic 2-spheres result to higher dimensional domains, that is we construct non-trivial, regular, n-harmonic n-spheres in suitable target manifolds. The proof follows a similar perturbative argument, which in high dimensions leads to a degenerate and double-phase-type Euler-Lagrange system, making the uniform regularity needed to formalise the bubbling harder to achieve. If time permits, we will sketch how to combine these results to solve quite general min-max problems for the n-energy modulo bubbling. This is a joint work with Tobias Lamm.

Umberto Guarnotta (Catania) – Seminario di Analisi

Martedì, 2 Dicembr – Sala Professori I livello ore 15:00 – 16:00

A p-LAPLACIAN PROBLEM IN RN WITH SINGULAR, CONVECTIVE, CRITICAL REACTION

This talk is devoted to discuss existence, regularity, and decay properties of solutions to a p-Laplacian problem set in the whole Euclidean space and exhibiting a critical term perturbed by a singular, convective reaction. The approach used combines variational methods, truncation techniques, and concentration compactness arguments, together with set-valued analysis and fixed point theory. De Giorgi’s technique, a priori gradient estimates, and nonlinear regularity theory are employed to obtain local Hölder regularity of gradients of solutions, as well as their pointwise decay at infinity. The result is new even in the non-singular case, also for the Laplacian.

Il professore Massimo Grossi dell’università di Roma la Sapienza il giorno giovedì 11 dicembre 2025 alle ore 15.00 nella sala riunioni del primo livello del dma terrà un seminario dal titolo:

Title: On the critical points of solutions of elliptic equations

Abstract: In this seminar we will study the shape of positive solutions to semilinear elliptic Dirichlet problems defined in a bounded domain of R^n. The first eigenfunction of the Laplacian and the solution to the torsion problem will serve as excellent toy models. A classical question we will address is the following: how does the geometry of the domain influence the number of critical points of the solutions?

We will also examine the case of Dirichlet problems on manifolds.