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Sobolev Problems with Spherical Mean Conditions and Traces of Quantized Canonical Transformations

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Abstract

We consider Sobolev problems (problems for an elliptic operator on a closed manifold with conditions on a closed submanifold) for the case in which these conditions are of nonlocal nature and include weighted spherical means of the unknown function over spheres of a given radius. For such problems, we establish a criterion for the Fredholm property and, in some special cases, obtain index formulas.

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Acknowledgement

The first author’s research was supported by the Ministry of Science and Higher Education within the framework of the Russian State Assignment under contract No. AAAA-A17-117021310377-1. The research of the second author was supported by RFBR grant 19-01-00574. The research of the third author was supported by RUDN University Program 5–100.

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Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526, Russia

    V. E. Nazaikinskii

  2. Peoples’ Friendship University of Russia (RUDN University), Moscow, 117198, Russia

    A. Yu. Savin & P. A. Sipailo

  3. Leibniz University of Hannover, Hannover, 30167, Germany

    A. Yu. Savin

Authors
  1. V. E. Nazaikinskii
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  2. A. Yu. Savin
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  3. P. A. Sipailo
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Corresponding authors

Correspondence to V. E. Nazaikinskii, A. Yu. Savin or P. A. Sipailo.

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To the memory of Mikhail Karasev

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Nazaikinskii, V.E., Savin, A.Y. & Sipailo, P.A. Sobolev Problems with Spherical Mean Conditions and Traces of Quantized Canonical Transformations. Russ. J. Math. Phys. 26, 483–498 (2019). https://doi.org/10.1134/S1061920819040071

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  • DOI: https://doi.org/10.1134/S1061920819040071

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