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Schauder estimates for boundary layer potentials

✍ Scribed by Michael Wiegner

Book ID
102948318
Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
611 KB
Volume
16
Category
Article
ISSN
0170-4214

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✦ Synopsis

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 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~.

📜 SIMILAR VOLUMES

Schauder Estimates for the Single Layer
Schauder Estimates for the Single Layer Potential in Hydrodynamics
✍ Paul Deuring; Werner Varnhorn 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 544 KB

## Abstract Let Ω be an open set in ℝ^__N__^(__N__ ⩾ 3), with compact boundary ϑΩ of type __C__^1,α^(ϵ(0,1)). We show that the single layer potential __Ef__, related to the stationary Stokes system on Ω, belongs to __C__^1,α^(ϑΩ)^__N__^, provided the source density __f__ belongs to __C__^α^(ϑΩ)^__N