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arXiv · 1902.05314

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

Iwona Chlebicka
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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 \[-{\rm div}\, a(x,Du)+b(x,u)=\mu\] 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.

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Iwona Chlebicka. 2019-02-14. Regularizing effect of the lower-order terms in elliptic problems with Orlicz growth. https://arxiv.org/abs/1902.05314

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