Toward the theory of the Dirichlet problem for the Beltrami equations

TitleToward the theory of the Dirichlet problem for the Beltrami equations
Publication TypeJournal Article
Year of Publication2015
AuthorsGutlyanskii, VYa., Ryazanov, VI, Yakubov, E
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2015.11.023
Issue11
SectionMathematics
Pagination23-29
Date Published11/2015
LanguageEnglish
Abstract

The Dirichlet problem for the degenerate Beltrami equations in arbitrary finitely connected domains is studied. In terms of the tangent dilatations, a series of criteria for the existence of regular solutions in arbitrary simply connected domains, as well as pseudoregular and multivalent solutions in arbitrary finitely connected domains without degenerate boundary components, are formulated.
KeywordsBeltrami equations, Dirichlet problem, finitely connected domains, prime ends, pseudoregular and multivalent solutions, regular solutions, simply connected domains
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