Schauder estimates for boundary layer potentials
Michael Wiegner · Mathematical Methods in the Applied Sciences · 1993
Abstract Boundary 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 type equation image with |ρ| odd and a density λ of class Ck+α. This paper presents a self‐contained exposition of the fact that the potential v may be continued as Ck+α‐functions onto G and ℝn\G respectively (together with estimates for the Hölder‐norms) under the least possible regularity assumption for the boundary ∂G: it has to be of class Ck+1+α.