Dirichlet problem with measurable data for semilinear equations in the plane

• Published in: Доповіді НАН України
• Date: 2022
• Main Authors: Gutlyanskiĭ, V.Ya., Nesmelova, O.V., Ryazanov, V.I., Yefimushkin, A.S.
• Format: Article
• Language: English
• Published: Видавничий дім "Академперіодика" НАН України 2022
• Subjects: Математика
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/184925
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Dirichlet problem with measurable data for semilinear equations in the plane / V.Ya. Gutlyanskiĭ, O.V. Nesmelova, V.I. Ryazanov, A.S. Yefimushkin // Доповіді Національної академії наук України. — 2022. — № 1. — С. 11-19. — Бібліогр.: 15 назв. — англ.

The study of the Dirichlet problem with arbitrary measurable data for harmonic functions in the unit disk D goes to the known dissertation of Luzin. His result was formulated in terms of angular limits (along nontangent paths) that are a traditional tool for the research of the boundary behavior i...