Finsler $p$-Laplace equation with a potential: Maz'ya-type
characterization and attainments of the Hardy constant
Finsler $p$-Laplace equation with a potential: Maz'ya-type
characterization and attainments of the Hardy constant
We study positive properties of the quasilinear elliptic equation $$-\mathrm{div}\mathcal{A}(x,\nabla u)+V|u|^{p-2}u=0\quad (1<p<\infty)\qquad \mbox{ in } \Omega,$$ where the function $\mathcal{A}(x,\xi)$ is induced by a family of norms on $\mathbb{R}^{n}$ ($n\geq 2$) parameterized by points in the domain $\Omega\subseteq\mathbb{R}^{n}$, and $V$ belongs to a certain local Morrey space. We first establish …