On a shape derivative result for the Robin p-Laplace eigenvalue problem
DOI:
https://doi.org/10.12775/TMNA.2026.001Keywords
$p$-Laplacian, eigenvalue problem, Robin boundary condition, shape derivative, Hadamard's perturbations, domain monotonicityAbstract
We obtain shape derivative formulae for the first eigenvalue of the Robin $p$-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.References
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