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arXiv · 2305.19672

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

Massimo Lanza de Cristoforis
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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.~G\"{u}nter, 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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Massimo Lanza de Cristoforis. 2023-05-31. Continuity of the double layer potential of a second order elliptic differential operator in Schauder spaces on the boundary. https://arxiv.org/abs/2305.19672

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