# Strong uniqueness for Dirichlet operators with singular potentials

V Liskevich, O Us

Research output: Chapter in Book/Report/Conference proceedingChapter in a book

## Abstract

We study the problem of strong uniqueness in L2 for the Dirichlet operator perturbed by a singular complex-valued potential. We reveal sufficient conditions on the logarithmic derivative ß of the measure pdx and the potential q, which ensure that the operator $$(\Delta + \beta \cdot\nabla - q) \upharpoonright C_0 ^\infty (\mathbb{R}^d )$$ has a unique extension generating a C0-semigroup on L2. The method of a-priori estimates of solutions of the corresponding elliptic equations is employed.
Translated title of the contribution Strong uniqueness for Dirichlet operators with singular potentials English Partial Differential Equations and Spectral Theory PDE2000 Conference in Clausthal, Germany Birkhäuser Basel 215-221 7 9783034882316 9783034894838 https://doi.org/10.1007/978-3-0348-8231-6_24 Published - 2001

### Publication series

Name Operator Theory: Advances and Applications Springer 126 0255-0156

### Bibliographical note

Publisher: Birkhauser