Opuscula Math. 38, no. 5 (2018), 733-758
https://doi.org/10.7494/OpMath.2018.38.5.733
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.
