171 research outputs found
Entropy solutions for the p(x)-Laplace equation
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 L1 data, extending the work of B´enilan et al. [5] to nonconstant exponents, as
well as integrability results for the solution and its gradient. The proofs rely crucially on a
priori estimates in Marcinkiewicz spaces with variable exponentCMUC/FCT and MCYT grants BMF2002-
04613-C03, MTM2005-07660-C02 (first author); CMUC/FCT and Project POCI/MAT/57546/2004 (second author
On the well-posedness of a two-phase minimization problem
We prove a series of results concerning the emptiness and non-emptiness
of a certain set of Sobolev functions related to the well-posedness of a two-phase
minimization problem, involving both the p(x)-norm and the in nity norm. The
results, although interesting in their own right, hold the promise of a wider applicability
since they can be relevant in the context of other problems where minimization
of the p-energy in a part of the domain is coupled with the more local minimization
of the L1-norm on another regio
The obstacle problem for nonlinear elliptic equations with variable growth and L1-data
The aim of this paper is twofold: to prove, for L1-data, the existence and
uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations
with variable growth, and to show some convergence and stability properties of the corresponding
coincidence set. The latter follow from extending the Lewy–Stampacchia inequalities
to the general framework of L
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