Numerical analysis of nonlinear elliptic-parabolic problems with variable exponent and L^1 data

Abstract

In this paper, we make the numerical analysis of the mild solution of elliptic-parabolic problem with variable exponent and L 1 -data. The functional setting involves Lebesgue and Sobolev spaces with variable exponents.

The obstacle problem for noncoercive elliptic equations with variable growth and $L^1$-data

“…The inequality of Lewy-Stampacchia in the general framework has been considered in numerous papers, see for example [15,[21][22][23][24][25][26]. In particular, the authors of [23] and [22] have proved the Lewy-Stampacchia inequalities for pseudomonotone elliptic operators in the context of variable exponent Sobolev spaces.…”