Regularity and symmetry results for nonlinear degenerate elliptic equations

In this paper we prove regularity results for a class of nonlinear degenerate elliptic equations of the form −div(A(|∇u|)∇u)+B(|∇u|)=f(u); in particular, we investigate the second order regularity of the solutions. As a consequence of these results, we obtain symmetry and monotonicity properties of...

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Bibliographic Details
Published in:Journal of Differential Equations 2022-11, Vol.336, p.315-333
Main Authors: Esposito, Francesco, Sciunzi, Berardino, Trombetta, Alessandro
Format: Article
Language:English
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Summary:In this paper we prove regularity results for a class of nonlinear degenerate elliptic equations of the form −div(A(|∇u|)∇u)+B(|∇u|)=f(u); in particular, we investigate the second order regularity of the solutions. As a consequence of these results, we obtain symmetry and monotonicity properties of positive solutions for this class of degenerate problems in convex symmetric domains via a suitable adaption of the celebrated moving plane method of Alexandrov-Serrin.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2022.07.021