In this paper we prove regularity results for a class of nonlinear degenerateelliptic equations of the form $displaystyle -operatorname{div}(A(|ablau|)abla u)+Bleft( |abla u|ight) =f(u)$; in particular, we investigatethe second order regularity of the solutions. As a consequence of theseresults, we obtain symmetry and monotonicity properties of positive solutionsfor this class of degenerate problems in convex symmetric domains via asuitable adaption of the celebrated moving plane method of Alexandrov-Serrin.

Regularity and symmetry results for nonlinear degenerate elliptic equations

Francesco Esposito
;
Berardino Sciunzi;Alessandro Trombetta
2022-01-01

Abstract

In this paper we prove regularity results for a class of nonlinear degenerateelliptic equations of the form $displaystyle -operatorname{div}(A(|ablau|)abla u)+Bleft( |abla u|ight) =f(u)$; in particular, we investigatethe second order regularity of the solutions. As a consequence of theseresults, we obtain symmetry and monotonicity properties of positive solutionsfor this class of degenerate problems in convex symmetric domains via asuitable adaption of the celebrated moving plane method of Alexandrov-Serrin.
2022
Mathematics - Analysis of PDEs
Mathematics - Analysis of PDEs
35B06, 35B50, 35B51
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/327428
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