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arXiv · 2102.07715

Regularity and symmetry results for nonlinear degenerate elliptic equations

Francesco Esposito·Berardino Sciunzi·Alessandro Trombetta
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Abstract

In this paper we prove regularity results for a class of nonlinear degenerate elliptic equations of the form $\displaystyle -\operatorname{div}(A(|\nabla u|)\nabla u)+B\left( |\nabla u|\right) =f(u)$; 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.

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Francesco Esposito, Berardino Sciunzi, Alessandro Trombetta. 2021-02-15. Regularity and symmetry results for nonlinear degenerate elliptic equations. https://arxiv.org/abs/2102.07715

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