Strong uniqueness for Dirichlet operators with singular potentials

V Liskevich, O Us

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


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 contributionStrong uniqueness for Dirichlet operators with singular potentials
Original languageEnglish
Title of host publicationPartial Differential Equations and Spectral Theory
Subtitle of host publicationPDE2000 Conference in Clausthal, Germany
PublisherBirkhäuser Basel
Number of pages7
ISBN (Electronic)9783034882316
ISBN (Print)9783034894838
Publication statusPublished - 2001

Publication series

NameOperator Theory: Advances and Applications
ISSN (Print)0255-0156

Bibliographical note

Publisher: Birkhauser

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