Semilinear equations in a plane and quasiconformal mappings

TitleSemilinear equations in a plane and quasiconformal mappings
Publication TypeJournal Article
Year of Publication2017
AuthorsGutlyanskii, VYa., Nesmelova, OV, Ryazanov, VI
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2017.01.010
Issue1
SectionMathematics
Pagination10-16
Date Published1/2017
LanguageEnglish
Abstract

We consider generalizations of the Bieberbach equation with nonlinear right parts, which makes it possible to study many problems of mathematical physics in inhomogeneous and anisotropic media with smooth characteristics. We establish interconnections of these semilinear equations with quasiconformal mappings, obtain on this basis, a series of theorems on the existence of their solutions that blow-up on the boundary of a unit disk, as well as on punctured unit disks and rings, and give their explicit representations.
KeywordsBeltrami equation, Bieberbach equation, Keller– Osserman condition, quasiconformal mappings, semilinear elliptic equations
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