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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:
It is part of: Transactions of the American Mathematical Society, 2009, vol. 361, num. 12, p. 6387-6405
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ISSN: 0002-9947
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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