EIGENVALUES OF THE FINSLER p‐LAPLACIAN ON VARYING DOMAINS

We study the dependence of the first eigenvalue of the Finsler p-Laplacian and the corresponding eigenfunctions on perturbation of the domain and we generalize a few results known for the standard p-Laplacian. In particular, we prove a Frechét differentiability result for the eigenvalues, compute the corresponding Hadamard formulas and prove a continuity result for the eigenfunctions. Finally, we briefly discuss a well-known overdetermined problem and we show how to deduce the Rellich–Pohozaev identity for the Finsler p-Laplacian from the Hadamard formula