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

2024/09/17 by de Cristoforis, Massimo Lanza
#31B10 #35J25 #35J25. 31B10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.11132

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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