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Abstract:

In this paper we study the behavior as p→∞ of solutions up,q to −Δpu−Δqu=0 in a bounded smooth domain Ω with a Lipschitz Dirichlet boundary datum u=g on ∂Ω. We find that there is a uniform limit of a subsequence of solutions, that is, there is pj→∞ such that upj,q→u∞ uniformly in Ω¯ and we prove that this limit u∞ is a solution to a variational problem, that, when the Lipschitz constant of the boundary datum is less than or equal to one, is given by the minimization of the Lq-norm of the gradient with a pointwise constraint on the gradient. In addition we show that the limit is a viscosity solution to a limit PDE problem that involves the q-Laplacian and the ∞-Laplacian. © 2016 Elsevier Ltd

Registro:

Documento: Artículo
Título:The behavior of solutions to an elliptic equation involving a p-Laplacian and a q-Laplacian for large p
Autor:Bonheure, D.; Rossi, J.D.
Filiación:Département de Mathématique, Université libre de Bruxelles, CP 214, Boulevard du Triomphe, Bruxelles, B-1050, Belgium
INRIA - Team MEPHYSTO, Belgium
Departamento de Matemática, FCEyN UBA, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina
Palabras clave:p-Laplacian; Viscosity solutions; Nonlinear equations; Viscosity; Behavior of solutions; Dirichlet boundary; Elliptic equations; Lipschitz constant; P-Laplacian; Smooth domains; Variational problems; Viscosity solutions; Laplace transforms
Año:2017
Volumen:150
Página de inicio:104
Página de fin:113
DOI: http://dx.doi.org/10.1016/j.na.2016.11.001
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_v150_n_p104_Bonheure

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Citas:

---------- APA ----------
Bonheure, D. & Rossi, J.D. (2017) . The behavior of solutions to an elliptic equation involving a p-Laplacian and a q-Laplacian for large p. Nonlinear Analysis, Theory, Methods and Applications, 150, 104-113.
http://dx.doi.org/10.1016/j.na.2016.11.001
---------- CHICAGO ----------
Bonheure, D., Rossi, J.D. "The behavior of solutions to an elliptic equation involving a p-Laplacian and a q-Laplacian for large p" . Nonlinear Analysis, Theory, Methods and Applications 150 (2017) : 104-113.
http://dx.doi.org/10.1016/j.na.2016.11.001
---------- MLA ----------
Bonheure, D., Rossi, J.D. "The behavior of solutions to an elliptic equation involving a p-Laplacian and a q-Laplacian for large p" . Nonlinear Analysis, Theory, Methods and Applications, vol. 150, 2017, pp. 104-113.
http://dx.doi.org/10.1016/j.na.2016.11.001
---------- VANCOUVER ----------
Bonheure, D., Rossi, J.D. The behavior of solutions to an elliptic equation involving a p-Laplacian and a q-Laplacian for large p. Nonlinear Anal Theory Methods Appl. 2017;150:104-113.
http://dx.doi.org/10.1016/j.na.2016.11.001