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Schauder Estimates for the Single Layer Potential in Hydrodynamics

✍ Scribed by Paul Deuring; Werner Varnhorn

Book ID
102943397
Publisher
John Wiley and Sons
Year
1992
Tongue
English
Weight
544 KB
Volume
157
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let Ξ© be an open set in ℝ^N^(N β©Ύ 3), with compact boundary ϑΩ of type C^1,Ξ±^(Ο΅(0,1)). We show that the single layer potential Ef, related to the stationary Stokes system on Ξ©, belongs to C^1,Ξ±^(ϑΩ)^N^, provided the source density f belongs to C^Ξ±^(ϑΩ)^N^. In addition, we prove a related estimate of the function E(f)~ϑΩ~ and its tangential derivatives.

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