Merouani Boubakeur, Zoubai Fayrouz: A nonlinear elasticity system in Sobolev spaces with variable exponents, 17-33

Abstract:

Several authors studied the system of elasticity with laws of particular behavior and using various techniques in constant exponents Sobolev spaces. In this article we consider a Dirichlet problem for nonlinear elasticity system with laws of general behavior. The coefficients of elasticity depends on $x$ and the density of the volumetric forces depends on the displacement. We consider this problem as a Leray-Lions operator and the main aim of this paper is to apply Galerkin techniques and monotone operator theory to prove a theorem of existence and uniqueness.

Key Words: Existence and uniqueness, spaces of Lebesgue and Sobolev with variable exponents, Dirichlet problem, nonlinear elasticity system, operator of Leray-Lions.

2010 Mathematics Subject Classification: Primary 35J45; Secondary 35J55, 35A05, 35A07, 35A15.