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

2019/02/14 by Chlebicka, Iwona
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.05314

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 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.

Related

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• Lipschitz regularity results for nonlinear strictly elliptic equations\n and applications
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