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Bonder, J.F.; Martínez, S.; Wolanski, N. "A free boundary problem for the p (x)-Laplacian" (2009) Nonlinear Analysis, Theory, Methods and Applications. 72(2):1078-1103
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Abstract:

We consider the optimization problem of minimizing ∫ Ω frac(1, p (x)) | ∇ u | p (x) + λ (x) χ {u > 0} d x in the class of functions W 1, p ({dot operator}) (Ω) with u - φ 0 ∈ W 0 1, p ({dot operator}) (Ω), for a given φ 0 ≥ 0 and bounded. W 1, p ({dot operator}) (Ω) is the class of weakly differentiable functions with ∫ Ω | ∇ u | p (x) d x < ∞. We prove that every solution u is locally Lipschitz continuous, that it is a solution to a free boundary problem and that the free boundary, Ω ∩ ∂ {u > 0}, is a regular surface. © 2009 Elsevier Ltd. All rights reserved.

Registro:

Documento: Artículo
Título:A free boundary problem for the p (x)-Laplacian
Autor:Bonder, J.F.; Martínez, S.; Wolanski, N.
Filiación:Departamento de Matemática, FCEyN UBA, 1428 Buenos Aires, Argentina
Palabras clave:Free boundaries; Minimization; Variable exponent spaces; Differentiable functions; Free boundary; Free-boundary problems; Lipschitz continuous; Optimization problems; P (x)-Laplacian; Regular surfaces; Optimization
Año:2009
Volumen:72
Número:2
Página de inicio:1078
Página de fin:1103
DOI: http://dx.doi.org/10.1016/j.na.2009.07.048
Título revista:Nonlinear Analysis, Theory, Methods and Applications
Título revista abreviado:Nonlinear Anal Theory Methods Appl
ISSN:0362546X
CODEN:NOAND
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v72_n2_p1078_Bonder

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Citas:

---------- APA ----------
Bonder, J.F., Martínez, S. & Wolanski, N. (2009) . A free boundary problem for the p (x)-Laplacian. Nonlinear Analysis, Theory, Methods and Applications, 72(2), 1078-1103.
http://dx.doi.org/10.1016/j.na.2009.07.048
---------- CHICAGO ----------
Bonder, J.F., Martínez, S., Wolanski, N. "A free boundary problem for the p (x)-Laplacian" . Nonlinear Analysis, Theory, Methods and Applications 72, no. 2 (2009) : 1078-1103.
http://dx.doi.org/10.1016/j.na.2009.07.048
---------- MLA ----------
Bonder, J.F., Martínez, S., Wolanski, N. "A free boundary problem for the p (x)-Laplacian" . Nonlinear Analysis, Theory, Methods and Applications, vol. 72, no. 2, 2009, pp. 1078-1103.
http://dx.doi.org/10.1016/j.na.2009.07.048
---------- VANCOUVER ----------
Bonder, J.F., Martínez, S., Wolanski, N. A free boundary problem for the p (x)-Laplacian. Nonlinear Anal Theory Methods Appl. 2009;72(2):1078-1103.
http://dx.doi.org/10.1016/j.na.2009.07.048