H²-regularity on convex domains for Robin eigenfunctions with parameter of arbitrary sign

2025/07/22 by Pier Domenico Lamberti, Luigi Provenzano, Lamberti, Pier Domenico +1
Mathematics · #35B65 #35P05 #35P15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2507.16726

openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Robin eigenfunctions on convex domains of \mathbb Rⁿ are H² 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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