In this paper, we prove a comparison principle for sub-supersolutions to a singular quasilinear problem that involves the anisotropic Finsler operator -Delta(H )(p)u := -div(Hp-1(del u) del H(del u)). As a main consequence, we obtain a uniqueness result for weak solutions to the problem (P). The proof is carried out also proving a sharp regularity result of the solutions up to the boundary. Our results are new even in the euclidean case.

A comparison principle for a doubly singular quasilinear anisotropic problem

Montoro, Luigi;Sciunzi, Berardino
;
Trombetta, Alessandro
2024-01-01

Abstract

In this paper, we prove a comparison principle for sub-supersolutions to a singular quasilinear problem that involves the anisotropic Finsler operator -Delta(H )(p)u := -div(Hp-1(del u) del H(del u)). As a main consequence, we obtain a uniqueness result for weak solutions to the problem (P). The proof is carried out also proving a sharp regularity result of the solutions up to the boundary. Our results are new even in the euclidean case.
2024
Comparison principle
Finsler anisotropic operator
Picone identity
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/363380
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