Continuity of the double layer potential of a second order elliptic differential operator in Schauder spaces on the boundary

2023/05/31 by Massimo Lanza de Cristoforis, de Cristoforis, Massimo Lanza
Computer Science · Mathematics · #31B10 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2305.19672

openalex publication_date 2023/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the validity of a regularizing property on the boundary of the double layer potential associated to the fundamental solution of a \em nonhomogeneous second order elliptic differential operator with constant coefficients in Schauder spaces of exponent greater or equal to two that sharpens classical results of N.M.~Günter, S.~Mikhlin, V.D.~Kupradze, T.G.~Gegelia, M.O.~Basheleishvili and T.V.~Bur\-chuladze, U.~Heinemann and extends the work of A.~Kirsch who has considered the case of the Helmholtz operator.

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