Estimates for the Counting Function of the Laplace Operator on Domains with Rough Boundaries

  • Yuri Netrusov
  • Yuri Safarov
Part of the International Mathematical Series book series (IMAT, volume 13)


We present explicit estimates for the remainder in the Weyl formula for the Laplace operator on a domain Ω, which involve only the most basic characteristics of Ω and hold under minimal assumptions about the boundary \(\partial \Omega\).


Laplace Operator Lipschitz Domain Essential Spectrum Planar Domain Counting Function 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BristolBristolUK
  2. 2.Department of MathematicsKing’s College London, StrandLondonUK

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