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Bounds for solutions of a class of quasilinear elliptic boundary value problems in terms of the torsion function

Published online by Cambridge University Press:  14 November 2011

L. E. Payne
L. E. Payne
Affiliation:
Forschungsinstitut für Mathematik ETH, Zürich and Cornell University, Ithaca, N.Y., U.S.A.
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Synopsis

In this paper maximum principles are employed to relate solutions of certain classes of nonlinear elliptic problems to solutions of the associated torsion problem. By this method a number of new isoperimetric inequalities are derived. In special cases solutions of the nonlinear problems are also related to solutions of the clamped membrane problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 88 , Issue 3-4 , 1981 , pp. 251 - 265
Copyright
Copyright © Royal Society of Edinburgh 1981

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