Gradient estimates for non-uniformly elliptic problems with BMO nonlinearity

We provide a new approach to obtain Calderon-Zygmund type estimates for non-uniformly elliptic equations with discontinuous nonlinearities of double phase growth. This approach, which is based on a small higher integrability result for the gradient of weak solutions to the associated homogeneous problems together with extrapolation from Muckenhoupt weights, enables us to find a proper comparison estimate of approximation by imposing merely a small BMO assumption on the nonlinearity with respect to the x-variable. As a consequence, we are able to prove an optimal regularity theory for a larger class of double phase problems with discontinuous nonlinearities in the literature.(c) 2022 Elsevier Inc. All rights reserved.