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dc.contributor.author
Lederman, Claudia Beatriz
dc.contributor.author
Wolanski, Noemi Irene
dc.date.available
2018-08-15T04:08:13Z
dc.date.issued
2016-06
dc.identifier.citation
Lederman, Claudia Beatriz; Wolanski, Noemi Irene; An inhomogeneous singular perturbation problem for the p(x)-Laplacian; Pergamon-Elsevier Science Ltd; Journal Of Nonlinear Analysis; 138; 6-2016; 300-325
dc.identifier.issn
0362-546X
dc.identifier.uri
http://hdl.handle.net/11336/55547
dc.description.abstract
In this paper we study the following singular perturbation problem for the pϵ(x)-Laplacian: Δpϵ (x)uϵ:=div(|∇uϵ(x)|pϵ (x)-2∇ uϵ)=βϵ(uϵ)+fϵ,uϵ≥0, (Pϵ(fϵ, pϵ)) where ϵ>0, βϵ(s)=1/ϵβ(s/ϵ), with β a Lipschitz function satisfying β>0 in (0,1), β≡0 outside (0,1) and ∫β(s)ds=M. The functions uϵ, fϵ and pϵ are uniformly bounded. We prove uniform Lipschitz regularity, we pass to the limit (ϵ→0) and we show that, under suitable assumptions, limit functions are weak solutions to the free boundary problem: u≥0 and {Δp(x)u = f in {u>0}u=0,|∇u|=λ ∗(x)on ∂{u>0} (P(f, p, λ∗)) with λ∗ (x)=(p(x)/p(x)-1 M)1/p(x), p = lim pϵ and f = lim fϵ. In Lederman and Wolanski (submitted) we prove that the free boundary of a weak solution is a C1,α surface near flat free boundary points. This result applies, in particular, to the limit functions studied in this paper.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Pergamon-Elsevier Science Ltd
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Free Boundary Problem
dc.subject
Singular Perturbation
dc.subject
Variable Exponent Spaces
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
An inhomogeneous singular perturbation problem for the p(x)-Laplacian
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-08-14T14:00:12Z
dc.journal.volume
138
dc.journal.pagination
300-325
dc.journal.pais
Países Bajos
dc.journal.ciudad
Amsterdam
dc.description.fil
Fil: Lederman, Claudia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
dc.description.fil
Fil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
dc.journal.title
Journal Of Nonlinear Analysis
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0362546X15003338
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1016/j.na.2015.09.026
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