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.File in questo prodotto:
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