$H^2$-regularity on convex domains for Robin eigenfunctions with parameter of arbitrary sign

Pier Domenico Lamberti; Luigi Provenzano

$H^2$-regularity on convex domains for Robin eigenfunctions with parameter of arbitrary sign

Analysis of PDEs 2025-07-23 v1

Authors: Pier Domenico Lamberti , Luigi Provenzano

Abstract

We prove that the Robin eigenfunctions on convex domains of $\mathbb R^n$ are $H^2$ regular regardless of the sign of the parameter involved in the boundary conditions. The proof is an adaptation of a classical argument used in the case of positive parameters combined with a Rellich-Pohozaev identity.

Keywords

Robin eigenfunctions $H^2$ regularity convex domains boundary conditions Rellich-Pohozaev identity

Cite

@article{arxiv.2507.16726,
  title  = {$H^2$-regularity on convex domains for Robin eigenfunctions with parameter of arbitrary sign},
  author = {Pier Domenico Lamberti and Luigi Provenzano},
  journal= {arXiv preprint arXiv:2507.16726},
  year   = {2025}
}

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