Maximal Differentiability for a General Class of Quasilinear Elliptic Equations with Right-hand Side Measures

Namkyeong Cho, Sun-Sig Byun, Ho-Sik Lee

Abstract: We prove maximal differentiability for the gradient of solutions to a certain type of nonlinear elliptic equations with a measure on the right-hand side. Our results generalize the limiting case of Calderón–Zygmund theory for an elliptic equation with p-growth to the case of Orlicz growth.