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

Ludovic Dan Lemle (1, 2)

1 ICJ - Institut Camille Jordan
2 Faculte d'Ingenierie de Hunedoara

Consider the Schrödinger 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 Schrödinger operators which is equivalent to the $L^1(D,dx)$-uniqueness of weak solutions of the heat diffusion equation associated to the operator $\cal A$.

Mots clés: $C_0$-semigroups; $L^\infty$-uniqueness of Schrödinger operators; $L^1$-uniqueness of the heat diffusion equation.; $L^1$-uniqueness of the heat diffusion equation

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Ludovic Dan Lemle. $L^\infty$-uniqueness of Schrödinger operators restricted in an open domain. 2008. ⟨hal-00197157v2⟩