Semilinear equations in the plane with measurable data

TitleSemilinear equations in the plane with measurable data
Publication TypeJournal Article
Year of Publication2018
AuthorsGutlyanskii, VYa., Nesmelova, OV, Ryazanov, VI
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2018.02.012
Issue2
SectionMathematics
Pagination12-18
Date Published2/2018
LanguageEnglish
Abstract

We study semilinear partial differential equations in the plane, the linear part of which is written in a divergence form. The main result is given as a factorization theorem. This theorem states that every weak solution of such an equation can be represented as a composition of a weak solution of the corresponding isotropic equation in a canonical domain and a quasiconformal mapping agreed with a matrix-valued measurable coefficient appearing in the divergence part of the equation. The latter makes it possible, in particular, to remove the regularity restrictions on the boundary in the study of boundary-value problems for such semilinear equations.
KeywordsBeltrami equation, quasiconformal mappings, semilinear elliptic equations
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