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

Pier Domenico Lamberti; Luigi Provenzano

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arXiv · 2507.16726

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

Pier Domenico Lamberti·Luigi Provenzano

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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.

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Pier Domenico Lamberti, Luigi Provenzano. 2025-07-22. $H^2$-regularity on convex domains for Robin eigenfunctions with parameter of arbitrary sign. https://arxiv.org/abs/2507.16726

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