A GLOBAL AND POINTWISE GRADIENT ESTIMATE FOR SOLUTIONS TO DOUBLE-PHASE PROBLEMS IN ORLICZ SPACES

Tóm tắt

The aim of this paper is twofold. Firstly, we give a global estimate of the Calderón-Zygmund type for solutions to double-phase problems in Orlicz spaces via maximal fractional functions. In this study, we employ the approach based on a generalized good-λ technique developed by Tran and Nguyen (2019), where regularity results are preserved under the fractional maximal operator. This operator is notable for its role in evaluating the oscillation of functions, and there is a close relation between this operator and the Riesz potential. Secondly, we present a pointwise estimate of the Riesz potential as a consequence of the first result.