On a shape derivative formula for the Robin $p$-Laplace eigenvalue
Analysis of PDEs
2024-01-17 v2
Abstract
We obtain shape derivative formulae for the first eigenvalue of the Robin -Laplace operator. This result is used to study the variation of the first eigenvalue with respect to perturbations of the domain. In particular, we prove that for large values of the boundary parameter, the first eigenvalue is monotonic with respect to domain inclusion for smooth domains.
Cite
@article{arxiv.2208.05183,
title = {On a shape derivative formula for the Robin $p$-Laplace eigenvalue},
author = {Ardra A and Mohan Mallick and Sarath Sasi},
journal= {arXiv preprint arXiv:2208.05183},
year = {2024}
}