**abstract:**
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 version
of 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.*

Thu 21 Sep, 15:30 - 16:30, Aula Dini

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