On the Boundary Behavior for the Blow-up Solutions of the sinh-Gordon Equation and Rank N Toda Systems in Bounded Domains-Reference-Cited by-同舟云学术

On the Boundary Behavior for the Blow-up Solutions of the sinh-Gordon Equation and Rank N Toda Systems in Bounded Domains

Published:2018-11-07 Issue:23 Volume:2020 Page:9386-9419
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Ao Weiwei¹,Jevnikar Aleks²^ORCID,Yang Wen³^ORCID

Affiliation:

1. Department of Mathematics and Statistics, Wuhan University, Wuhan, P.R. China

2. Department of Mathematics, University of Pisa, Largo Bruno Pontecorvo, Pisa, Italy

3. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, P.O. Box, Wuhan, P. R. China

Abstract

Abstract In this paper we are concerned with the blow-up analysis of two classes of problems in bounded domains arising in mathematical physics: sinh-Gordon equation and some general rank $n$ Toda systems. The presence of a residual mass in the blowing up limit makes the analysis quite delicate; nevertheless, by exploiting suitable Pohozaev identities and a detailed blow-up analysis we exclude blowup at the boundary. This is the 1st result in this direction in the presence of a residual mass. As a byproduct we obtain general existence results in bounded domains.

Funder

National Natural Science Foundation of China

PRIN12 project: Variational and Perturbative Aspects of Nonlinear Differential Problems

FIRB project: Analysis and Beyond

Center for Advanced Study

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2020/23/9386/34659468/rny263.pdf

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