The log-Sobolev inequality for the ground state of a Schrödinger operator on bounded convex domains

Huaiqian Li, Dejun Luo

We consider the ground state ${\varphi }_0$ of the Schrödinger operator $L=-\Delta +V$ on the bounded convex domain $\Omega \subset {\mathbb{R}}^n$, satisfying the Dirichlet boundary condition. Assume that $V\in…