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Under various conditions on the data we analyze how the appearance of lower order terms affects the gradient estimates on solutions to a general nonlinear elliptic equation of the form $$- {\rm{div}}\;a\left( {x,Du} \right) + b\left( {x,u} \right) = \mu$$ with data μ 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.

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