Higher differentiability for solutions of a general class of nonlinear elliptic obstacle problems with Orlicz growth

Namkyeong Cho, Sun-Sig Byun

Abstract: In this paper we study a general class of nonlinear elliptic obstacle problems with Orlicz growth. Our purpose is to prove maximal differentiability of the gradient of solutions in the scale of both fractional Sobolev spaces and Besov spaces. Our regularity results extend the known higher differentiability results for such problems with polynomial growth to those with Orlicz growth.