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Partial Differential Equations and Spectral Theory pp 215–221Cite as

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Strong Uniqueness for Dirichlet Operators with Singular Potentials

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 126))

Abstract

We study the problem of strong uniqueness in L 2 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 C 0 -semigroup on L 2. The method of a-priori estimates of solutions of the corresponding elliptic equations is employed.

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References

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Author information

Authors and Affiliations

  1. Vitali Liskevich, Oleksiy US, School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK

    Vitali Liskevich & Oleksiy Us

Authors
  1. Vitali Liskevich
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  2. Oleksiy Us
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, TU Clausthal, Erzstr. 1, Clausthal-Zellerfeld, 38678, Germany

    Michael Demuth

  2. Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, Potsdam, 14469, Germany

    Bert-Wolfgang Schulze

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© 2001 Springer Basel AG

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Liskevich, V., Us, O. (2001). Strong Uniqueness for Dirichlet Operators with Singular Potentials. In: Demuth, M., Schulze, BW. (eds) Partial Differential Equations and Spectral Theory. Operator Theory: Advances and Applications, vol 126. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8231-6_24

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  • DOI: https://doi.org/10.1007/978-3-0348-8231-6_24

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9483-8

  • Online ISBN: 978-3-0348-8231-6

  • eBook Packages: Springer Book Archive

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