Concentrated terms and varying domains in elliptic equations: Lipschitz case

Concentrated terms and varying domains in elliptic equations: Lipschitz case

Author Aragao, Gleiciane S. Autor UNIFESP Google Scholar
Bruschi, Simone M. Google Scholar
Abstract In this paper, we analyze the behavior of a family of solutions of a nonlinear elliptic equation with nonlinear boundary conditions, when the boundary of the domain presents a highly oscillatory behavior, which is uniformly Lipschitz and nonlinear terms, are concentrated in a region, which neighbors the boundary of domain. We prove that this family of solutions converges to the solutions of a limit problem in H(1)an elliptic equation with nonlinear boundary conditions which captures the oscillatory behavior of the boundary and whose nonlinear terms are transformed into a flux condition on the boundary. Indeed, we show the upper semicontinuity of this family of solutions.Copyright (c) 2015 John Wiley & Sons, Ltd.
Keywords semilinear elliptic equations
nonlinear boundary value problems
varying boundary
oscillatory behavior
concentrated terms
upper semicontinuity of solutions
xmlui.dri2xhtml.METS-1.0.item-coverage Hoboken
Language English
Sponsor CNPq, Brazil
Grant number CNPq: 475146/2013-1
Date 2016
Published in Mathematical Methods In The Applied Sciences. Hoboken, v. 39, n. 12, p. 3450-3460, 2016.
ISSN 0170-4214 (Sherpa/Romeo, impact factor)
Publisher Wiley-Blackwell
Extent 3450-3460
Access rights Closed access
Type Article
Web of Science ID WOS:000379947400022

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