### Abstract

Original language | English |
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Pages (from-to) | 273-318 |

Journal | St. Petersburg Mathematical Journal |

Issue number | 2 |

Publication status | Published - 2015 |

### Cite this

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**Asymptotic expansions for eigenvalues of the Steklov problem in singularly perturbed domains.** / Nazarov, S.A.

Research output › › peer-review

TY - JOUR

T1 - Asymptotic expansions for eigenvalues of the Steklov problem in singularly perturbed domains

AU - Nazarov, S.A.

PY - 2015

Y1 - 2015

N2 - © 2015 American Mathematical Society.Full asymptotic expansions are constructed and justified for two series of eigenvalues and the corresponding eigenfunctions of the spectral Steklov problem in a domain with a singular boundary perturbation having the form of a small cavity. The terms of those series are of type λk+o(1) and ε-1(μm+o(1)), where λk and μm are the eigenvalues of the Steklov problem in a bounded domain without cavity and the exterior Steklov problem for a cavity of unit size. A similar problem of the surface wave is also treated. The smoothness requirements on the boundary are discussed and unsolved problems are stated.

AB - © 2015 American Mathematical Society.Full asymptotic expansions are constructed and justified for two series of eigenvalues and the corresponding eigenfunctions of the spectral Steklov problem in a domain with a singular boundary perturbation having the form of a small cavity. The terms of those series are of type λk+o(1) and ε-1(μm+o(1)), where λk and μm are the eigenvalues of the Steklov problem in a bounded domain without cavity and the exterior Steklov problem for a cavity of unit size. A similar problem of the surface wave is also treated. The smoothness requirements on the boundary are discussed and unsolved problems are stated.

M3 - Article

SP - 273

EP - 318

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 2

ER -