Estimates of singular numbers (s-numbers) for a class of degenerate elliptic operators
Өзгешеленетiн эллиптикалық операторлардың бiр класы үшiн сингулярлық сандарды (s-сандарды) бағалау
Оценки сингулярных чисел (s-чисел) для одного класса вырождающихся эллиптических операторов
Igisinov S.Zh. Zhumaliyeva L.D. Suleimbekova A.O. Bayandiyev Ye.N.
2022E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2022#107Issue 351 - 58 pp.
In this paper we study a class of degenerate elliptic equations with an arbitrary power degeneracy on the line. Based on the research carried out in the course of the work, the authors propose methods to overcome various difficulties associated with the behavior of functions from the definition domain for a differential operator with piecewise continuous coefficients in a bounded domain, which affect the spectral characteristics of boundary value problems for degenerate elliptic equations. It is shown the conditions imposed on the coefficients at the lowest terms of the equation, which ensure the existence and uniqueness of the solution. The existence, uniqueness, and smoothness of a solution are proved, and estimates are found for singular numbers (s-numbers) and eigenvalues of the semiperiodic Dirichlet problem for a class of degenerate elliptic equations with arbitrary power degeneration.
boundary value problem , elliptic operator , power degeneracy , singular numbers , solution , uniqueness
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M.Kh. Dulaty Taraz Regional University, Taraz, Kazakhstan
M.Kh. Dulaty Taraz Regional University
10 лет помогаем публиковать статьи Международный издатель
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