Weyl asymptotics for Poincaré–Steklov eigenvalues in a domain with  Lipschitz boundary

Rozenblum, Grigori

doi:10.4171/jst/477

J. Spectr. Theory

2023

DOI: 10.4171/jst/477

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Weyl asymptotics for Poincaré–Steklov eigenvalues in a domain with Lipschitz boundary

Grigori Rozenblum

Abstract: We justify the Weyl asymptotic formula for the eigenvalues of the Poincaré-Steklov spectral problem for a domain bounded by a Lipschitz surface.In the memory of Mikhail Birman and Mikhail Solomyak, my teachers 2020 Mathematics Subject Classification. Primary 35P20; Secondary 35J25.

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Weyl’s Law for the Steklov Problem on Surfaces with Rough Boundary

Karpukhin

Lagacé

Polterovich

2023

Arch Rational Mech Anal

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The validity of Weyl’s law for the Steklov problem on domains with Lipschitz boundary is a well-known open question in spectral geometry. We answer this question in two dimensions and show that Weyl’s law holds for an even larger class of surfaces with rough boundaries. This class includes domains with interior cusps as well as “slow” exterior cusps. Moreover, the condition on the speed of exterior cusps cannot be improved, which makes our result, in a sense optimal. The proof is based on the methods of Suslina and Agranovich combined with some observations about the boundary behaviour of conformal mappings.

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Weyl’s Law for the Steklov Problem on Surfaces with Rough Boundary

Karpukhin

Lagacé

Polterovich

2023

Arch Rational Mech Anal

View full text Add to dashboard Cite

show abstract

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Weyl asymptotics for Poincaré–Steklov eigenvalues in a domain with Lipschitz boundary

Abstract: We justify the Weyl asymptotic formula for the eigenvalues of the Poincaré-Steklov spectral problem for a domain bounded by a Lipschitz surface.In the memory of Mikhail Birman and Mikhail Solomyak, my teachers 2020 Mathematics Subject Classification. Primary 35P20; Secondary 35J25.

Cited by 1 publication

References 40 publications

Weyl’s Law for the Steklov Problem on Surfaces with Rough Boundary

Weyl’s Law for the Steklov Problem on Surfaces with Rough Boundary

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