By using a priori estimates and the Riesz theorem, we investigate a boundary-value problem for nonuniformly 2b -elliptic equations with arbitrary power singularities in the coefficients of the equation and boundary conditions on a certain set of points. We establish the existence and obtain an integral representation of the unique solution of the formulated boundary-value problem in Hölder spaces with power weights whose order is determined via the orders of singularities in the coefficients of the equation and boundary conditions.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 64, No. 3, pp. 16–25, July–September, 2021.
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Luste, I.P., Pukal’s’kyi, I.D. Boundary-Value Problem for Nonuniformly Elliptic Equations with Power Singularities. J Math Sci 278, 748–760 (2024). https://doi.org/10.1007/s10958-024-06959-8
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DOI: https://doi.org/10.1007/s10958-024-06959-8