Estimates of Eigenvalues of a Semiperiodic Dirichlet Problem for a Class of Degenerate Elliptic Equations
In this paper, we consider a class of degenerate elliptic equations with arbitrary power degeneration. The issues about the existence, uniqueness, and smoothness of solutions of the semiperiodic Dirichlet problem for a class of degenerate elliptic equations with arbitrary power degeneration are stud...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/4/692 |
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| author | Mussakan Muratbekov Sabit Igissinov |
| author_facet | Mussakan Muratbekov Sabit Igissinov |
| author_sort | Mussakan Muratbekov |
| collection | DOAJ |
| description | In this paper, we consider a class of degenerate elliptic equations with arbitrary power degeneration. The issues about the existence, uniqueness, and smoothness of solutions of the semiperiodic Dirichlet problem for a class of degenerate elliptic equations with arbitrary power degeneration are studied. The two-sided estimates for singular numbers (s-numbers) are obtained. Note that estimates of singular numbers (s-numbers) show the rate of approximation of the found solutions by finite-dimensional subspaces. Here, we also obtain estimates for the eigenvalues. We note that, in this paper, apparently, two-sided estimates of singular numbers (s-numbers) for degenerate elliptic operators are obtained for the first time. At the end of the paper, a symmetric operator is considered, i.e., a self-adjoint case. |
| first_indexed | 2024-03-09T04:12:14Z |
| format | Article |
| id | doaj.art-f4095699f53144eea4f2de1aba581333 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T04:12:14Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-f4095699f53144eea4f2de1aba5813332023-12-03T13:59:58ZengMDPI AGSymmetry2073-89942022-03-0114469210.3390/sym14040692Estimates of Eigenvalues of a Semiperiodic Dirichlet Problem for a Class of Degenerate Elliptic EquationsMussakan Muratbekov0Sabit Igissinov1Department of Mathematics, M.Kh. Dulaty Taraz Regional University, Taraz 080000, KazakhstanDepartment of Mathematics, M.Kh. Dulaty Taraz Regional University, Taraz 080000, KazakhstanIn this paper, we consider a class of degenerate elliptic equations with arbitrary power degeneration. The issues about the existence, uniqueness, and smoothness of solutions of the semiperiodic Dirichlet problem for a class of degenerate elliptic equations with arbitrary power degeneration are studied. The two-sided estimates for singular numbers (s-numbers) are obtained. Note that estimates of singular numbers (s-numbers) show the rate of approximation of the found solutions by finite-dimensional subspaces. Here, we also obtain estimates for the eigenvalues. We note that, in this paper, apparently, two-sided estimates of singular numbers (s-numbers) for degenerate elliptic operators are obtained for the first time. At the end of the paper, a symmetric operator is considered, i.e., a self-adjoint case.https://www.mdpi.com/2073-8994/14/4/692degenarate elliptic operatorboundary value problemsingular numberspower degenerationsolutionuniqueness |
| spellingShingle | Mussakan Muratbekov Sabit Igissinov Estimates of Eigenvalues of a Semiperiodic Dirichlet Problem for a Class of Degenerate Elliptic Equations Symmetry degenarate elliptic operator boundary value problem singular numbers power degeneration solution uniqueness |
| title | Estimates of Eigenvalues of a Semiperiodic Dirichlet Problem for a Class of Degenerate Elliptic Equations |
| title_full | Estimates of Eigenvalues of a Semiperiodic Dirichlet Problem for a Class of Degenerate Elliptic Equations |
| title_fullStr | Estimates of Eigenvalues of a Semiperiodic Dirichlet Problem for a Class of Degenerate Elliptic Equations |
| title_full_unstemmed | Estimates of Eigenvalues of a Semiperiodic Dirichlet Problem for a Class of Degenerate Elliptic Equations |
| title_short | Estimates of Eigenvalues of a Semiperiodic Dirichlet Problem for a Class of Degenerate Elliptic Equations |
| title_sort | estimates of eigenvalues of a semiperiodic dirichlet problem for a class of degenerate elliptic equations |
| topic | degenarate elliptic operator boundary value problem singular numbers power degeneration solution uniqueness |
| url | https://www.mdpi.com/2073-8994/14/4/692 |
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