Geodesic
Asymptotics of the spectrum of a boundary-value problem with the Steklov condition on small sets periodically distributed along a contour
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 51, Tome 536 (2024), pp. 178-227

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We construct asymptotics of eigenvalues of the Laplace equation in a multi-dimesional domain with the spectral Steklov conditions on small identical sets distributed frequently and periodically along a smooth closed contour at a planar part of the boundary while its remaining part is supplied with the Dirichlet condition. We describe the localization effect for the eigenfunctions near the contour. The limiting spectral problem implies an ordinary differential equation at the contour whose coefficients depend quadratically on its curature. Asymptotic structures in the three-dimensional domain differ from other dimensions because they become dependent on logarithm of the small parameter, namely the period of distribution of the Steklov “spots”. 
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     author = {S. A. Nazarov},
     title = {Asymptotics of the spectrum of a boundary-value problem with the {Steklov} condition on small sets periodically distributed along a contour},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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S. A. Nazarov. Asymptotics of the spectrum of a boundary-value problem with the Steklov condition on small sets periodically distributed along a contour. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 51, Tome 536 (2024), pp. 178-227. http://geodesic.mathdoc.fr/item/ZNSL_2024_536_a9/