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On the method of moving planes and the sliding method

On the method of moving planes and the sliding method The method of moving planes and the sliding method are used in proving monotonicity or symmetry in, say, thex 1 direction for solutions of nonlinear elliptic equationsF(x, u, Du, D 2 u)=0 in a bounded domain Ω in ℝ n which is convex in thex 1 direction. Here we present a much simplified approach to these methods; at the same time it yields improved results. For example, for the Dirichlet problem, no regularity of the boundary is assumed. The new approach relies on improved forms of the Maximum Principle in “narrow domains”. Several results are also presented in cylindrical domains—under more general boundary conditions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

On the method of moving planes and the sliding method

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References (14)

Publisher
Springer Journals
Copyright
Copyright © 1991 by Sociedade Brasileira de Matemática
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/BF01244896
Publisher site
See Article on Publisher Site

Abstract

The method of moving planes and the sliding method are used in proving monotonicity or symmetry in, say, thex 1 direction for solutions of nonlinear elliptic equationsF(x, u, Du, D 2 u)=0 in a bounded domain Ω in ℝ n which is convex in thex 1 direction. Here we present a much simplified approach to these methods; at the same time it yields improved results. For example, for the Dirichlet problem, no regularity of the boundary is assumed. The new approach relies on improved forms of the Maximum Principle in “narrow domains”. Several results are also presented in cylindrical domains—under more general boundary conditions.

Journal

Bulletin of the Brazilian Mathematical Society, New SeriesSpringer Journals

Published: Feb 16, 2005

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