Gradient estimates for problems with Orlicz growth
Iwona Chlebicka
TL;DR
This paper investigates gradient estimates for nonlinear elliptic equations with Orlicz growth, providing new Lorentz and Morrey space bounds for solutions' gradients under various data conditions.
Contribution
It introduces novel gradient estimates in Lorentz and Morrey spaces for elliptic equations with Orlicz growth, extending existing regularity results.
Findings
Established Lorentz-type gradient bounds.
Derived Morrey-type estimates for solutions.
Extended regularity theory for Orlicz growth problems.
Abstract
We study a general nonlinear elliptic equation in the Orlicz setting with data not belonging to the dual of the energy space. We provide several Lorentz-type and Morrey-type estimates for the gradients of solutions under various conditions on the data.
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