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Boundedness of the extremal solution of some p-Laplacian problems
Sanchón, ManelIn this article we consider the p-Laplace equation on a smooth bounded domain of with zero Dirichlet boundary conditions. Under adequate assumptions on f we prove that the extremal solution of this problem is in the energy class independently of the domain. We also obtain Lq and W1,q estimates for such a solution. Moreover, we prove its boundedness for some range of dimensions depending on the nonlinearity f. ...
The obstacle problem for nonlinear elliptic equations with variable growth and ...
Rodrigues, José Francisco; Sanchón, Manel; Urbano, José MiguelThe 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 L1
Regularity of entropy solutions of quasilinear elliptic problems related with H...
Abdellaoui, Boumediene; Colorado, Eduardo; Sanchón, ManelCMUC/FCT; MEC Spanish grant MTM2004-02223, MTM2004-02223, BFM2003-03772, BMF2002-04613- C03, MTM2005-07660-C02-01
Semi-stable and extremal solutions of reaction equations involving the p-laplacian
Cabré, Xavier; Sanchón, ManelWe consider nonnegative solutions of −_pu = f(x, u), where p > 1 and _p is the p-Laplace operator, in a smooth bounded domain of RN with zero Dirichlet boundary conditions. We introduce the notion of semi-stability for a solution (perhaps unbounded). We prove that certain minimizers, or one-sided minimizers, of the energy are semi-stable, and study the properties of this class of solutions. Under some assumptio...
Entropy solutions for the p(x)-Laplace equation
Sanchón, Manel; Urbano, José MiguelWe 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 exponent ...
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