arXiv:2409.11132 Abstract | arXiv Analytics

arXiv:2409.11132 [math.AP]Abstract References Reviews Resources

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

Published 2024-09-17Version 1

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.

Comments: arXiv admin note: substantial text overlap with arXiv:2408.17192; text overlap with arXiv:2309.00393, arXiv:2307.04775, arXiv:2305.19672

Categories: math.AP

Subjects: 31B10, 35J25, 31B10, 35J25, 31B10, 35J25, 31B10, 35J25

Keywords: schauder spaces, limiting case, double layer potential, second order differential operator, nonzero natural number

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