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The Krein–von Neumann Realization of Perturbed Laplacians on Bounded Lipschitz Domains

  • Jussi BehrndtEmail author
  • Fritz Gesztesy
  • Till Micheler
  • Marius Mitrea
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 255)

Abstract

In this paper we study the self-adjoint Krein–von Neumann realization A k of the perturbed Laplacian \(-\Delta\;+\;V\) in a bounded Lipschitz domain \(\Omega\;\subset\;\mathbb{R}^n\). We provide an explicit and self-contained description of the domain of A k in terms of Dirichlet and Neumann boundary traces, and we establish a Weyl asymptotic formula for the eigenvalues of A k.

Keywords

Lipschitz domains Krein Laplacian trace maps eigenvalues spectral analysis Weyl asymptotics. 

Mathematics Subject Classification (2010).

Primary 35J25 35P20 Secondary 35P05 46E35 47F05 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Jussi Behrndt
    • 1
    Email author
  • Fritz Gesztesy
    • 2
  • Till Micheler
    • 3
  • Marius Mitrea
    • 2
  1. 1.Institut für Numerische MathematikTechnische Universität GrazGrazAustria
  2. 2.Department of MathematicsUniversity of MissouriColumbiaUSA
  3. 3.Department of MathematicsTechnische Universität BerlinBerlinGermany

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