Irina Nenciu
University of Illinois at Chicago, Chicago, USA

We consider the problem of essential self-adjointness of the drift-diffusion operator $H=-\frac{1}{\rho}\nabla\cdot \rho \mathbb D\nabla +V$ on domains $\Omega \subset \mathbb R^d$. We give criteria showing how the behavior as $x \rightarrow \partial \Omega$ of the coefficients $\rho$, $\mathbb D$, and $V$ balances to ensure essential self-adjointness of $H$ by using a new, weak anisotropic Hardy inequality. This talk is based on joint work with G. Nenciu (IMAR).