Schauder estimates for boundary layer potentials

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 C k+α . This paper presents a self‐contained exposition of the fact that the potential v may be continued as C k+α ‐functions onto G and ℝ n respectively (together with estimates for the Hölder‐norms) under the least possible regularity assumption for the boundary ∂ G : it has to be of class C k+1+α .