Gradient integrability estimates for elliptic double-obstacle problems with degenerate matrix weights

Abstract

The main objective of this paper is to study a regularity estimate for solutions to a certain elliptic double-obstacle problem involving $p$-Laplacian with degenerate weights. Motivated by the recent advances in this topic, we derive a general decay estimate for level sets of solutions’ gradients, toward understanding the regularity properties of obstacle problems involving a matrix-valued weight. In turn, it allows us to establish global norm estimates in a variety of specific families of spaces.