Artículo
Mercaldo, A.; Rossi, J.D.; De León, S.S.; Trombetti, C. "On the behaviour of solutions to the Dirichlet problem for the p(x)-Laplacian when p(x) goes to 1 in a subdomain" (2012) Differential and Integral Equations. 25(1-2):53-74
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Abstract:
In this paper we prove a stability result for some classes of elliptic problems involving variable exponents. More precisely, we consider the Dirichlet problem for an elliptic equation in a domain, which is the p-Laplacian equation, -div(∇up-2∇u) = f, in a subdomain Ω1 of Ω and the Laplace equation, -Δu = f, in its complementary (that is, our equation involves the so-called p(x)-Laplacian with a discontinuous exponent). We assume that the right-hand side f belongs to L∞(Ω). For this problem, we study the behaviour of the solutions as p goes to 1, showing that they converge to a function u, which is almost everywhere finite when the size of the datum f is small enough. Moreover, we prove that this u is a solution of a limit problem involving the 1-Laplacian operator in Ω1. We also discuss uniqueness under a favorable geometry.
Registro:
| Documento: | Artículo |
| Título: | On the behaviour of solutions to the Dirichlet problem for the p(x)-Laplacian when p(x) goes to 1 in a subdomain |
| Autor: | Mercaldo, A.; Rossi, J.D.; De León, S.S.; Trombetti, C. |
| Filiación: | Dipartimento di Matematica e Applicazioni R. Caccioppoli, Università di Napoli Federico II, Complesso Monte S. Angelo, Via Cintia, 80126 Napoli, Italy Departamento de Análisis Matemático, Universidad de Alicante, Ap. correos 99, 03080 Alicante, Spain Departament d'Análisi Matemática, Universitat de Valéncia, Dr. Moliner 50, 46100 Burjassot, Valéncia, Spain Departamento de Matemática, FCEyN UBA, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina |
| Año: | 2012 |
| Volumen: | 25 |
| Número: | 1-2 |
| Página de inicio: | 53 |
| Página de fin: | 74 |
| Título revista: | Differential and Integral Equations |
| Título revista abreviado: | Differ. Integr. Equ. |
| ISSN: | 08934983 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08934983_v25_n1-2_p53_Mercaldo |
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Citas:
---------- APA ----------
Mercaldo, A., Rossi, J.D., De León, S.S. & Trombetti, C. (2012) . On the behaviour of solutions to the Dirichlet problem for the p(x)-Laplacian when p(x) goes to 1 in a subdomain. Differential and Integral Equations, 25(1-2), 53-74.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08934983_v25_n1-2_p53_Mercaldo [ ]
---------- CHICAGO ----------
Mercaldo, A., Rossi, J.D., De León, S.S., Trombetti, C. "On the behaviour of solutions to the Dirichlet problem for the p(x)-Laplacian when p(x) goes to 1 in a subdomain" . Differential and Integral Equations 25, no. 1-2 (2012) : 53-74.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08934983_v25_n1-2_p53_Mercaldo [ ]
---------- MLA ----------
Mercaldo, A., Rossi, J.D., De León, S.S., Trombetti, C. "On the behaviour of solutions to the Dirichlet problem for the p(x)-Laplacian when p(x) goes to 1 in a subdomain" . Differential and Integral Equations, vol. 25, no. 1-2, 2012, pp. 53-74.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08934983_v25_n1-2_p53_Mercaldo [ ]
---------- VANCOUVER ----------
Mercaldo, A., Rossi, J.D., De León, S.S., Trombetti, C. On the behaviour of solutions to the Dirichlet problem for the p(x)-Laplacian when p(x) goes to 1 in a subdomain. Differ. Integr. Equ. 2012;25(1-2):53-74.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08934983_v25_n1-2_p53_Mercaldo [ ]
