Calculus of Variations and Geometric Measure Theory

G. Paoli - G. Piscitelli - L. Trani

Sharp estimates for the first $p$-Laplacian eigenvalue and for the $p$-torsional rigidity on convex sets with holes

created by piscitelli on 31 Aug 2022
modified on 11 Sep 2022



Inserted: 31 aug 2022
Last Updated: 11 sep 2022

Year: 2019

ArXiv: 1908.00362 PDF


We study, in dimension $n\geq2$, the eigenvalue problem and the torsional rigidity for the $p$-Laplacian on convex sets with holes, with external Robin boundary conditions and internal Neumann boundary conditions. We prove that the annulus maximizes the first eigenvalue and minimizes the torsional rigidity when the measure and the external perimeter are fixed.