Descrizione

Alba Lia Masiello (UniNa)

“Estimates for Robin p-Laplacian eigenvalues of convex sets with prescribed perimeter”

We will consider the shape optimization problem of minimizing/maximizing

the first eigenvalue of the p-Laplace operator with Robin boundary

conditions in the class of convex sets. In particular, when imposing a

perimeter constraint, we will study the behavior of the eigenvalues as

the boundary parameter beta varies in R. We prove an upper bound for the

first Robin eigenvalue of the p-Laplacian with a positive boundary parameter and a quantitative

versionof the reverse Faber-Krahn type inequality for the first Robin eigenvalue of the

p-Laplacian with negative boundary parameter, making use of a comparison

argument obtained by means of inner parallel sets.

The results are contained in a joint work with V. Amato and A. Gentile.

Vincenzo Amato (UniNa)

“Somea symptotic quantitative inequalities”.

Abstract:The classical quantitative isoperimetric inequality has opened the way for a rich line of research into quantitative versions of many inequalities. In practice, such an inequality aims to estimate how much a set with an almost minimal perimeter must be ‘similar’ to a ball.

We will discuss the case where a spectral inequality is not achieved. In particular, we will analyse the case of two inequalities, one concerning torsional rigidity and the other the first non-trivial Neumann eigenvalue, both of which are asymptotically achieved by a sequence of thinning rectangles.

Joint works with D. Bucur, A.L. Masiello, G. Paoli and R. Sannipoli.