A Limiting Case of a Theorem of C. Miranda for Layer Potentials in Schauder Spaces

Massimo Lanza de Cristoforis ()
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Massimo Lanza de Cristoforis: Università di Padova, Dipartimento di Matematica ‘Tullio Levi-Civita’

Chapter Chapter 15 in Integral Methods in Science and Engineering, 2026, pp 211-231 from Springer

Abstract: 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 $$C^{m,1}$$ and the densities are of class C m −1 , 1 $$C^{m-1,1}$$ for the single layer potential and C m , 1 $$C^{m,1}$$ for the double layer potential for some nonzero natural number m. The treatment of the limiting case requires generalized Schauder spaces.

Date: 2026
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DOI: 10.1007/978-3-032-04458-7_15

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