Regularizing effect of the lower-order terms in elliptic problems with Orlicz growth

Abstract

Under various conditions on the data we analyse how appearence of lower order terms affects the gradient estimates on solutions to a general nonlinear elliptic equation of the form \[-{\rm div}\, a(x,Du)+b(x,u)=μ\] with data $\mu$ not belonging to the dual of the natural energy space but to Lorentz/Morrey-type spaces. The growth of the leading part of the operator is governed by a function of Orlicz-type, whereas the lower-order term satisfies the sign condition and is minorized with some convex function, whose speed of growth modulates the regularization of the solutions.

Continuation of arXiv:1805.11326 (which is published already DOI:10.1016/j.na.2018.10.008)