REGULARITY RESULTS FOR (p,q)-LAPLACE TYPE EQUATIONS IN GENERALIZED MORREY SPACES

Abstract

The quasi-linear non-uniformly elliptic problems were motivated by minimizing problems for non-standard integral energy functionals, which can be applied to many applications in sciences such as fluid dynamics, nonlinear elasticity, and physics. A typical example of this type of problem may be seen as the (p,q)-Laplace equation. In this paper, we establish some gradient estimates via fractional maximal operators for a class of (p,q)-Laplace type equations in generalized Morrey spaces. The global regularity results were obtained in two steps. In the first step, we construcedt the gradient estimate in the setting of weighted Lorentz spaces. The regularity result in Morrey spaces were obtained in the second step