Existence and regularity of solutions for nonlinear measure data problems with general growth

Sun-Sig Byun, Namkyeong Cho, Youn Yeonghun

Abstract: We investigate the existence of distributional solutions to nonlinear elliptic problems with general growth when the right-hand side is a bounded Radon measure. An optimal global Calderón-Zygmund type estimate for such problems is obtained by using mapping property of the fractional maximal function of the measure.