On a model semilinear elliptic equation in the plane
type: Item
instance of: scholarly article
title: On a model semilinear elliptic equation in the plane
zbMATH Open document ID: 1369.35015
published in: Journal of Mathematical Sciences (New York)
publication date: 2017-04-06T00:00:00Z
full work available at URL: http://dspace.nbuv.gov.ua/handle/123456789/140893
review text: This paper deals with the blow-up problem for a model semilinear equation of the type \[ \text{div}(A(z)\nabla u)= e^u \] in a simply connected domain \(\Omega\subset \mathbb{C}^1\). \(A(z)\) is a \(2\times 2\) symmetric uniformly elliptic matrix with measurable entries and \(\text{det\,}A=1\). The authors show that the Liouville-Bieberbach function solves the problem under consideration in the case when \(A\) is generated by a special Beltrami coefficient.
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35J61
Mathematics Subject Classification ID: 30C62
zbMATH DE Number: 6702003
zbMATH Keywords: semilinear elliptic equations
zbMATH Keywords: Bieberbach equation
zbMATH Keywords: quasiconformal mappings
zbMATH Keywords: Beltrami equation
author: Vladimir Gutlyanskiĭ
author: O. V. Nesmelova
author: Vladimir I. Ryazanov
reviewed by: Peter R. Popivanov
MaRDI profile type: Publication
OpenAlex ID: W2561788230
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DOI: 10.1007/S10958-016-3203-5
description: scientific article; zbMATH DE number 6702003