Файл	Ном	Сабт карда шуд
1-Байзаев Саттор	A PRIORI ESTIMATES FOR SECOND-ORDER ELLIPTIC OPERATORS IN HOLDER SPACES	39

Authors: Baizaev Sattor - Doctor of Physical and Mathematical Sciences, Professor of the Department of Mathematical Disciplines and Modern Natural Science, Tajik State University of Law, Business and Politics (Tajikistan Republic, Khujand). Barotov Ruziboy Numonjonovich - Doctoral Student (PhD) of the Mathematical Analysis Department named after Professor A. Muksinov under Khujand State University named after academician B.Gafurov (Tajikistan Republic, Khujand)

JOURNAL NUMBER: 4(67). YEAR OF ISSUE: 2023.LANGUAGE OF THE ARTICLE: Russian

ANNOTATION

The paper considers an elliptic operator, the main part of which is the Bitsadze operator, and the junior term consists of the product of a given matrix function by the conjugation of a vector function. The operator is studied in the Banach space of vector functions bounded and uniformly continuous by Helder in the entire complex plane. It turns out that the operator in the specified space may not be Noetherian, an example of an operator with infinite-dimensional kernel is given. For the case of coefficients weakly oscillating at infinity, conditions are found, written out in the language of the spectrum of limit matrices formed by partial limits of the matrix of coefficients at infinity, at which an a priori estimate takes place.

KEY WORDS

elliptic operator, Holder spaces, a priori estimates

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