HAL : hal-00402869, version 1
 DOI : 10.1016/j.na.2010.02.044
 Nonlinear Analysis: Theory, Methods and Applications A 72, 12 (2010) 4649-4660
 Structural stability for variable exponent elliptic problems. II. The $p(u)$-laplacian and coupled problems.
 (06/2010)
 We study well-posedness for elliptic problems under the form $$b(u)-\div \mathfrak{a}(x,u,\Grad u)=f,$$ where $\mathfrak{a}$ satisfies the classical Leray-Lions assumptionswith an exponent $p$ that may depend both on the space variable $x$ and on the unknown solution $u$. A prototype case is the equation $u-\div \Bigl( |\grad u|^{p(u)-2}\grad u \Bigr)=f$. We have to assume that $\inf_{x\in\overline{\Om},\,z\in\R} p(x,z)$ is greater than the space dimension $N$. Then, under mild regularity assumptions on $\Om$ and on the nonlinearities, we show that the associated solution operator is an order-preserving contraction in $L^1(\Om)$. In addition, existence analysis for a sample coupled system for unknowns $(u,v)$ involving the $p(v)$-laplacian of $u$ is carried out. Coupled elliptic systems with similar structure appear in applications, e.g. in modelling of stationary thermo-rheological fluids.
 1 : Laboratoire de Mathématiques (LM-Besançon) CNRS : UMR6623 – Université de Franche-Comté 2 : Centro de Investigación en Ingeniería Matemática [Concepción] (CI²MA) Universidad de Concepción 3 : LAME Ouagadougou, Burkina-Faso (LAME) Université de Ouagadougou
 Domaine : Mathématiques/Equations aux dérivées partielles
 Mots Clés : variable exponent – $p(u)$-laplacian – thermo-rheological fluids – well-posedness – Young measures
Liste des fichiers attachés à ce document :
 PDF
 Stab-part-II-pn_u_-ABO.pdf(324.4 KB)
 hal-00402869, version 1 http://hal.archives-ouvertes.fr/hal-00402869 oai:hal.archives-ouvertes.fr:hal-00402869 Contributeur : Boris Andreianov <> Soumis le : Mercredi 8 Juillet 2009, 15:14:33 Dernière modification le : Vendredi 23 Avril 2010, 11:59:17