Toward the theory of semi-linear equations

Autor:	Gutlyanskii, Vladimir, Nesmelova, Olga, Ryazanov, Vladimir
Rok vydání:	2017
Předmět:	Mathematics - Complex Variables 30C62 31A05 31A20 31A25 31B25 35J61 35Q15 (Primary) 30E25 31C05 34M50 35F45 (Secondary)
Druh dokumentu:	Working Paper
Popis:	In this paper we study the 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. Comment: 35 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1711.00041 Zobrazit plný text záznamu View this record from Arxiv