$L^\infty$-uniqueness of Schrödinger operators restricted in an open domain
Abstract
Description
Consider the Schrödinger operator ${\cal A}=-\fracΔ{2}+V$ acting on space $C_0^\infty(D)$, where $D$ is an open domain in $\R^d$. The main purpose of this paper is to present the $L^\infty(D,dx)$-uniqueness for Schrödinger operators which is equivalent to the $L^1(D,dx)$-uniqueness of weak solutions of the heat diffusion equation associated to the operator $\cal A$.