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arXiv · 2409.11132

A limiting case of a theorem of C. Miranda for layer potentials in Schauder spaces

Massimo Lanza de Cristoforis
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Abstract

The aim of this paper is to prove a theorem of C.~Miranda for the single and double layer potential corresponding to the fundamental solution of a second order differential operator with constant coefficients in Schauder spaces in the limiting case in which the open set is of class $C^{m,1}$ and the densities are of class $C^{m-1,1}$ for the single layer potential and of class $C^{m,1}$ for the double layer potential for some nonzero natural number $m$. The treatment of the limiting case requires generalized Schauder spaces.

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Massimo Lanza de Cristoforis. 2024-09-17. A limiting case of a theorem of C. Miranda for layer potentials in Schauder spaces. https://arxiv.org/abs/2409.11132

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