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Schauder estimates for boundary layer potentials
Author(s) -
Wiegner Michael
Publication year - 1993
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670161204
Subject(s) - mathematics , mathematical analysis , exposition (narrative) , class (philosophy) , boundary value problem , boundary (topology) , partial differential equation , boundary layer , type (biology) , image (mathematics) , differential equation , mixed boundary condition , layer (electronics) , pure mathematics , physics , thermodynamics , art , ecology , chemistry , literature , organic chemistry , artificial intelligence , biology , computer science
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 typewith |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 \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 C k+1+α .