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Abstract:

In this paper we study a one phase free boundary problem for the p (x)-Laplacian with non-zero right hand side. We prove that the free boundary of a weak solution is a C1,α surface in a neighborhood of every "flat" free boundary point. We also obtain further regularity results on the free boundary, under further regularity assumptions on the data. We apply these results to limit functions of an inhomogeneous singular perturbation problem for the p (x)-Laplacian that we studied in [25]. © European Mathematical Society 2017.

Registro:

Documento: Artículo
Título:Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the p (x)-Laplacian
Autor:Lederman, C.; Wolanski, N.
Filiación:IMAS, CONICET, Departamento de Mateḿatica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
Palabras clave:Free boundary problem; Inhomogeneous problem; Regularity of the free boundary; Singular perturbation; Variable exponent spaces
Año:2017
Volumen:19
Número:2
Página de inicio:201
Página de fin:241
DOI: http://dx.doi.org/10.4171/IFB/381
Título revista:Interfaces and Free Boundaries
Título revista abreviado:Interfaces Free Boundaries
ISSN:14639963
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_14639963_v19_n2_p201_Lederman

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Citas:

---------- APA ----------
Lederman, C. & Wolanski, N. (2017) . Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the p (x)-Laplacian. Interfaces and Free Boundaries, 19(2), 201-241.
http://dx.doi.org/10.4171/IFB/381
---------- CHICAGO ----------
Lederman, C., Wolanski, N. "Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the p (x)-Laplacian" . Interfaces and Free Boundaries 19, no. 2 (2017) : 201-241.
http://dx.doi.org/10.4171/IFB/381
---------- MLA ----------
Lederman, C., Wolanski, N. "Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the p (x)-Laplacian" . Interfaces and Free Boundaries, vol. 19, no. 2, 2017, pp. 201-241.
http://dx.doi.org/10.4171/IFB/381
---------- VANCOUVER ----------
Lederman, C., Wolanski, N. Weak solutions and regularity of the interface in an inhomogeneous free boundary problem for the p (x)-Laplacian. Interfaces Free Boundaries. 2017;19(2):201-241.
http://dx.doi.org/10.4171/IFB/381