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Abstract:

In this work we study a minimization problem with two-phases where in each phase region the problem is ruled by a quasi-linear elliptic operator of p-Laplacian type. The problem in its variational form is as follows: min R ?\\fv0g 1 p jrvjp C p C C fCv dx C R ?\\fv60g 1 q jrvjq C q C fv dx : Here we minimize among all admissible functions v in an appropriate Sobolev space with a prescribed boundary datum v D g on @?. First, we show existence of a minimizer, prove some properties, and provide an example for non-uniqueness. Moreover, we analyze the limit case where p and q go to infinity, obtaining a limiting free boundary problem governed by the 1Laplacian operator. Consequently, Lipschitz regularity for any limiting solution is obtained. Finally, we establish some weak geometric properties for solutions. © European Mathematical Society 2018.

Registro:

Documento: Artículo
Título:A limit case in non-isotropic two-phase minimization problems driven by p-Laplacians
Autor:Da Silva, J.V.; Rossi, J.D.
Filiación:Depto. Matematica, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria-Pabellón I-(C1428EGA), Buenos Aires, Argentina
Palabras clave:1 ∞ Laplacian; Free boundary problems; Non-isotropic two-phase problems
Año:2018
Volumen:20
Número:3
Página de inicio:379
Página de fin:406
DOI: http://dx.doi.org/10.4171/IFB/406
Título revista:Interfaces and Free Boundaries
Título revista abreviado:Interfaces Free Boundaries
ISSN:14639963
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14639963_v20_n3_p379_DaSilva

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Citas:

---------- APA ----------
Da Silva, J.V. & Rossi, J.D. (2018) . A limit case in non-isotropic two-phase minimization problems driven by p-Laplacians. Interfaces and Free Boundaries, 20(3), 379-406.
http://dx.doi.org/10.4171/IFB/406
---------- CHICAGO ----------
Da Silva, J.V., Rossi, J.D. "A limit case in non-isotropic two-phase minimization problems driven by p-Laplacians" . Interfaces and Free Boundaries 20, no. 3 (2018) : 379-406.
http://dx.doi.org/10.4171/IFB/406
---------- MLA ----------
Da Silva, J.V., Rossi, J.D. "A limit case in non-isotropic two-phase minimization problems driven by p-Laplacians" . Interfaces and Free Boundaries, vol. 20, no. 3, 2018, pp. 379-406.
http://dx.doi.org/10.4171/IFB/406
---------- VANCOUVER ----------
Da Silva, J.V., Rossi, J.D. A limit case in non-isotropic two-phase minimization problems driven by p-Laplacians. Interfaces Free Boundaries. 2018;20(3):379-406.
http://dx.doi.org/10.4171/IFB/406