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

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Abstract

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.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland

    Iwona Chlebicka

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  1. Iwona Chlebicka
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Correspondence to Iwona Chlebicka.

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The research is supported by NCN grant no. 2016/23/D/ST1/01072.

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Chlebicka, I. Regularizing effect of the lower-order terms in elliptic problems with Orlicz growth. Isr. J. Math. 236, 967–1000 (2020). https://doi.org/10.1007/s11856-020-1995-y

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