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Almgren-type monotonicity methods for the classification of behaviour at corners of solutions to semilinear elliptic equations

Published online by Cambridge University Press:  25 September 2013

Veronica Felli
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via Cozzi 53, 20125 Milano, Italy, (veronica.felli@unimib.it)
Alberto Ferrero
Affiliation:
Università degli Studi del Piemonte Orientale, Viale Teresa Michel 11, 15121 Alessandria, Italy, (alberto.ferrero@mfn.unipmn.it)

Abstract

A monotonicity approach to the study of the asymptotic behaviour near corners of solutions to semilinear elliptic equations in domains with a conical boundary point is discussed. The presence of logarithms in the first term of the asymptotic expansion is excluded for boundary profiles sufficiently close to straight conical surfaces.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2013 

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