A WEIGHTED LORENTZ ESTIMATE FOR DOUBLE-PHASE PROBLEMS

Abstract

Double-phase problems were modeled by minimizing the problems of a class of integral energy functionals with non-standard growth conditions. They have many applications in physics, such as nonlinear elasticity, fluid dynamics, and homogenization. The present paper provides a global gradient estimate for distribution solutions to double-phase problems in Lorentz spaces associated with a Muckenhoupt weight. In particular, this work is a weighted version of the main result found by Tran and Nguyen (2021). Our method is based on a construction of the weighted distribution inequality on fractional maximal operators, which have close relations to Riesz potential.