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Abstract:

In this paper we study the following problem. For ε > 0, take uε as a solution of Luε := div(g(ι∇u ει/ι∇uει)∇u ε) = βε(uε), u ε ≥ 0. A solution to (Pε) is a function uε Ε W1,G(Ω) ∩ L&infin(Ω) such that ∫ωg(ι∇uει) ∇u ε/ι∇uει ∇ℓ dx = ̄ ∫ω ℓβε(uε) dx for every ℓ Ε C&infin 0(Ω). Here βε (s) = 1/εβ(s/ε), with β Ε Lip(rdbl), β > 0in(0, 1) and β = 0 otherwise. We are interested in the limiting problem, when ε → 0. As in previous work with L = Δ or L = Δp we prove, under appropriate assumptions, that any limiting function is a weak solution to a free boundary problem. Moreover, for nondegenerate limits we prove that the reduced free boundary is a C 1, α surface. This result is new even for Δp. Throughout the paper, we assume that g satisfies the conditions introduced by Lieberman in [ Comm. Partial Differential Equations, 16 (1991), pp. 311-361]. © 2009 Society for Industrial and Applied Mathematics.

Registro:

Documento: Artículo
Título:A singular perturbation problem for A quasi-linear operator satisfying the natural growth condition of lieberman
Autor:Sandra, M.; Noemi, W.
Filiación:Departamento de Matemática, FCEyN, UBA, (1428) Buenos Aires, Argentina
Palabras clave:Free boundaries; Orlicz spaces; Singular perturbation; Following problem; Free boundary; Free-boundary problems; Growth conditions; Limiting problem; Orlicz spaces; Quasi-linear; Singular perturbation problems; Singular perturbations; Weak solution; Differential equations; Mathematical operators
Año:2009
Volumen:41
Número:1
Página de inicio:318
Página de fin:359
DOI: http://dx.doi.org/10.1137/070703740
Título revista:SIAM Journal on Mathematical Analysis
Título revista abreviado:SIAM J. Math. Anal.
ISSN:00361410
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361410_v41_n1_p318_Sandra

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Citas:

---------- APA ----------
Sandra, M. & Noemi, W. (2009) . A singular perturbation problem for A quasi-linear operator satisfying the natural growth condition of lieberman. SIAM Journal on Mathematical Analysis, 41(1), 318-359.
http://dx.doi.org/10.1137/070703740
---------- CHICAGO ----------
Sandra, M., Noemi, W. "A singular perturbation problem for A quasi-linear operator satisfying the natural growth condition of lieberman" . SIAM Journal on Mathematical Analysis 41, no. 1 (2009) : 318-359.
http://dx.doi.org/10.1137/070703740
---------- MLA ----------
Sandra, M., Noemi, W. "A singular perturbation problem for A quasi-linear operator satisfying the natural growth condition of lieberman" . SIAM Journal on Mathematical Analysis, vol. 41, no. 1, 2009, pp. 318-359.
http://dx.doi.org/10.1137/070703740
---------- VANCOUVER ----------
Sandra, M., Noemi, W. A singular perturbation problem for A quasi-linear operator satisfying the natural growth condition of lieberman. SIAM J. Math. Anal. 2009;41(1):318-359.
http://dx.doi.org/10.1137/070703740