$L^\infty$-uniqueness of Schrödinger operators restricted in an open domain

Details $L^\infty$-uniqueness of Schrödinger operators restricted in an open domain $L^\infty$-uniqueness of Schrödinger operators restricted in an open domain

2007-12-14

arxiv.org/abs/0712.2411v2

Physics

Mathematical Physics

Scientific paper

Consider the Schr\"odinger operator ${\cal A}=-\frac{\Delta}{2}+V$ 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 Schr\"odinger
operators which is equivalent to the $L^1(D,dx)$-uniqueness of weak solutions
of the heat diffusion equation associated to the operator $\cal A$.

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