Elliptic problems with nonstandard conditions of growth: Zhikov's approach
Yu. A. Alkhutov · Complex Variables and Elliptic Equations · 2011
This article is an overview of the basic notions pertaining to nonlinear p(x)-Laplacian elliptic equations, in particular, Sobolev spaces with variable exponent, regularity of integral functionals, conditions ensuring Hölder continuity of a solution and higher integrability of its gradient. Many of these notions were originally introduced by V.V. Zhikov.