Regularity of weak solutions to generalized quasilinear elliptic obstacle problems

Abstract

In this paper, the work is divided into two parts. First, we are interested in presenting some estimates involving the generalized ψ-Hilfer operator in the domain of the ball $B\left(R\right)$ by means of classical inequalities such as Young's, Holder's, and Harnack's. On the other hand, motivated by such results, we will investigate the $C^{1,\alpha }$-regularity of weak solutions for a new class of m-Laplacian obstacle problems with $C^{1,\bar{\beta }}$-obstacle function under controllable growth conditions in the ψ-fractional space.