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15.—Differentiability on the Boundary of the Solutions of Linear Elliptic Boundary Value Problems

Published online by Cambridge University Press:  14 February 2012

Renate Schappel
Renate Schappel
Affiliation:
Mathematisches Seminar, Frankfurt am Main
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Synopsis

The present paper is concerned with the problem of regularity of weak solutions of boundary value problems. We shall present a new method to prove differentiability on the boundary. This method was developed in our thesis [12] within the theory of abstract Sobolev spaces, introduced by Stummel [14]. Here, we shall describe it by applying it to elliptic boundary value problems. It will be seen that the advantage of this method consists in the fact that it is based on functional analysis only and therefore may be used for other types of differential equations as well.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 73 , 1975 , pp. 235 - 249
Copyright
Copyright © Royal Society of Edinburgh 1975

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