A quantization property for blow up solutions of singular Liouville-type equations
type: Item
instance of: scholarly article
title: A quantization property for blow up solutions of singular Liouville-type equations
zbMATH Open document ID: 1174.35379
published in: Journal of Functional Analysis
publication date: 2005-03-08T00:00:00Z
review text: The author considers a ``concentrating'' solution-sequence \(u_k\) satisfying \[ -\Delta u_k= |z|^{2\alpha_k} V_k(z) e^{u_k}\quad\text{in }\mathbb B_1, \] \[ |z|^{2\alpha_k} V_k(z) e^{u_k}\to \beta\delta_{z=0}\text{ weakly in the sense of measures in }\mathbb B_1, \] where \(\alpha_k\in \mathbb R^+\). Under some natural assumptions on \(\alpha_k\) and \(V)k(z)\), the author shows that necessarily \[ \beta\in 8\pi\,\mathbb N\cup\{8\pi(1+ \alpha)+ 8\pi \mathbb Z^+\}, \] where \(\alpha_k\to \alpha\). It is shown by explicit examples, that the obtained result is ``sharp''.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B60
zbMATH DE Number: 2141631
author: G. Tarantello
MaRDI profile type: Publication
full work available at URL: j.jfa.2004.07.006
OpenAlex ID: W2084799191
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DOI: 10.1016/J.JFA.2004.07.006
description: scientific article; zbMATH DE number 2141631