Opuscula Math. 38, no. 5 (2018), 733-758

Opuscula Mathematica

Eigenvalue asymptotics for potential type operators on Lipschitz surfaces of codimension greater than 1

Grigori Rozenblum
Grigory Tashchiyan

Abstract. For potential type integral operators on a Lipschitz submanifold the asymptotic formula for eigenvalues is proved. The reasoning is based upon the study of the rate of operator convergence as smooth surfaces approximate the Lipschitz one.

Keywords: integral operators, potential theory, eigenvalue asymptotics.

Mathematics Subject Classification: 47G40, 35P20.

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  • Grigori Rozenblum
  • Department of Mathematics, Chalmers University of Technology, Sweden
  • University of Gothenburg, Eklandagatan 86, S-412 96 Gothenburg, Sweden
  • Department of Physics, St. Petersburg State University, Russia
  • Grigory Tashchiyan
  • St. Petersburg University for Telecommunications, Department of Mathematics, St. Petersburg, 198504, Russia
  • Communicated by P.A. Cojuhari.
  • Received: 2017-12-14.
  • Accepted: 2017-12-27.
  • Published online: 2018-06-12.
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Cite this article as:
Grigori Rozenblum, Grigory Tashchiyan, Eigenvalue asymptotics for potential type operators on Lipschitz surfaces of codimension greater than 1, Opuscula Math. 38, no. 5 (2018), 733-758, https://doi.org/10.7494/OpMath.2018.38.5.733

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