Nonlinear elliptic systems with variable exponents and measure data

Abstract

In this paper we prove existence results for distributional solutions of nonlinear elliptic systems with a measure data. The functional setting involves Lebesgue-Sobolev spaces as well as weak Lebesgue (Marcinkiewicz) spaces with variable exponents W01,p(·)(Ω) and Mp(·)(Ω) respectively.

Nonlinear anisotropic elliptic equations in with variable exponents and locally integrable data

“…j j pj.x/ 1 1 A , i D 1, : : : , N, C > 0, existence and regularity results with L 1 -data have been obtained in [5] for a class of anisotropic elliptic equations. If the variable exponent p i ../ D p../ satisfies the log-Hölder continuity condition (9), similar results for the Dirichlet problem on a bounded domain are established in ( [6,7]). If p../ is assumed to be merely continuous function, the corresponding results for isotropic elliptic equations (or systems) are developed in [8,9].…”

“…If the variable exponent p i ../ D p../ satisfies the log-Hölder continuity condition (9), similar results for the Dirichlet problem on a bounded domain are established in ( [6,7]). If p../ is assumed to be merely continuous function, the corresponding results for isotropic elliptic equations (or systems) are developed in [8,9]. For the constant isotropic case, we refer the reader to [10] and the references therein.…”

“…We refer to [15,16] . /, but if the exponent variable p../ > 1 satisfies the log-Hölder continuity condition (9), that is,…”

“…If p (.) is assumed to be merely continuous function, the corresponding results for isotropic elliptic equations (or systems) are developed in . For the constant isotropic case, we refer the reader to and the references therein.…”

Infinitely Many Solutions of the Neumann Problem for Elliptic systems in Anisotropic Variable Exponent Sobolev Spaces

“…In the same case M. Bendahmane and F. Mokhtari have studied in [5] the problem (P) in the isotropic variable Sobolev space where the second term was a measure data. In the same framework, D. S. Moschetto in [15] have studied the problem (P) in the particular case of homogeneous Neumann condition and…”