# On the boundary behavior for the blow up solutions of the sinh-Gordon equation and rank $N$ Toda systems in bounded domains

created by jevnikar on 24 Oct 2016
modified on 04 Dec 2017

[BibTeX]

Preprint

Inserted: 24 oct 2016
Last Updated: 4 dec 2017

Year: 2017

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 blow up at the boundary. This is the first result in this direction in the presence of a residual mass. As a byproduct we obtain general existence results in bounded domains.