CRM: Centro De Giorgi
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A Pisan workshop in geometric analysis

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

speaker: Alba Lia Masiello (Università di Napoli Federico II )

abstract: We will consider the shape optimization problem of minimizingmaximizing 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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