Estimates of Eigenvalues of a Semiperiodic Dirichlet Problem for a Class of Degenerate Elliptic Equations
Muratbekov M. Igissinov S.
April 2022MDPI
Symmetry
2022#14Issue 4
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 semiperi-odic 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.
boundary value problem , degenarate elliptic operator , power degeneration , singular numbers , solution , uniqueness
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Department of Mathematics, M.Kh. Dulaty Taraz Regional University, Taraz, 080000, Kazakhstan
Department of Mathematics
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