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Type: Artigo de periódico
Title: Critical points of the regular part of the harmonic Green function with Robin boundary condition
Author: Davila, J
Kowalczyk, M
Montenegro, M
Abstract: In this paper we consider the Green function for the Laplacian in a smooth bounded domain Omega subset of R(N) with Robin boundary condition partial derivative G(lambda)/partial derivative nu + lambda b(x)G(lambda) = 0, on partial derivative Omega, and its regular part S(lambda)(x,y), where b > 0 is smooth. We show that in general, as lambda -> infinity, the Robin function R(lambda)(x) = S(lambda) (x, x) has at least 3 critical points. Moreover, in the case b equivalent to const we prove that R(lambda) has critical points near non-degenerate critical points of the mean curvature of the boundary, and when b not equivalent to const there are critical points of R(lambda) near non-degenerate critical points of b. (C) 2008 Elsevier Inc. All rights reserved.
Subject: Green's function
Regular part
Robin boundary condition
Critical points
Country: EUA
Editor: Academic Press Inc Elsevier Science
Citation: Journal Of Functional Analysis. Academic Press Inc Elsevier Science, v. 255, n. 5, n. 1057, n. 1101, 2008.
Rights: fechado
Identifier DOI: 10.1016/j.jfa.2007.11.023
Date Issue: 2008
Appears in Collections:Unicamp - Artigos e Outros Documentos

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