W1,p(·)-Regularity for a Class of Non-uniformly Elliptic Problems with Orlicz Growth

We prove a local W 1 , p ( · ) -regularity for the distributional solutions to double phase elliptic equations with Orlicz growth, and the variable exponents p ( x ) > 1 satisfying the log-Hölder continuity. Moreover, we establish a local Calderón–Zygmund estimate for asymptotically regular double phase elliptic problems with Orlicz growth, which means that the nonlinearity is getting close to the regular problems when the gradient of its solution goes to infinity.