Schauder estimates for boundary layer potentials

摘要

AbstractBoundary layer potentials with Hölder‐continuous densities are widely used for representing solutions of boundary value problems for certain partial differential equations. These potentials are of the typewith |ρ| odd and a density λ of classCk+α. This paper presents a self‐contained exposition of the fact that the potentialvmay be continued asCk+α‐functions ontoGandℝnGrespectively (together with estimates for the Hölder‐norms) under the least possible regularity assumption for the boundary ∂G: it has to