A comparison principle for a doubly singular quasilinear anisotropic problem

Abstract

In this paper, we prove a comparison principle for sub-supersolutions to a singular quasilinear problem that involves the anisotropic Finsler operator $$-{\mathrm{\Delta }}_p^{H}u:=-div(H^{p-1}(\nabla u)\nabla H(\nabla u)).$$ As a main consequence, we obtain a uniqueness result for weak solutions to the problem (℘). 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.