Classes of kernels and continuity properties of the double layer potential in Hölder spaces

2023/07/09 by Massimo Lanza de Cristoforis, de Cristoforis, M. Lanza
Computer Science · Mathematics · #31B10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2307.04775

openalex publication_date 2023/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the validity of regularizing properties of the boundary integral operator corresponding to the double layer potential associated to the fundamental solution of a \em nonhomogeneous second order elliptic differential operator with constant coefficients in Hölder spaces by exploiting an estimate on the maximal function of the tangential gradient with respect to the first variable of the kernel of the double layer potential and by exploiting specific imbedding and multiplication properties in certain classes of integral operators and a generalization of a result for integral operators on differentiable manifolds.

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