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http://hdl.handle.net/2445/96448
Title: | Entropy solutions for the $p(x)$-Laplace equations |
Author: | Sanchón, Manel Urbano, José Miguel |
Keywords: | Equacions en derivades parcials Operadors el·líptics Anàlisi funcional no lineal Partial differential equations Elliptic operator Nonlinear functional analysis |
Issue Date: | Dec-2009 |
Publisher: | American Mathematical Society (AMS) |
Abstract: | We consider a Dirichlet problem in divergence form with variable growth, modeled on the $ p(x)$-Laplace equation. We obtain existence and uniqueness of an entropy solution for $ L^1$ data, as well as integrability results for the solution and its gradient. The proofs rely crucially on a priori estimates in Marcinkiewicz spaces with variable exponent, for which we obtain new inclusion results of independent interest. |
Note: | Reproducció del document publicat a: http://dx.doi.org/10.1090/S0002-9947-09-04399-2 |
It is part of: | Transactions of the American Mathematical Society, 2009, vol. 361, num. 12, p. 6387-6405 |
URI: | http://hdl.handle.net/2445/96448 |
Related resource: | http://dx.doi.org/10.1090/S0002-9947-09-04399-2 |
ISSN: | 0002-9947 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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569721.pdf | 308.98 kB | Adobe PDF | View/Open |
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