Calculus of Variations and Geometric Measure Theory

W. Ao - A. Jevnikar - W. Yang

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 10 Oct 2018


Accepted Paper

Inserted: 24 oct 2016
Last Updated: 10 oct 2018

Journal: Intern. Math. Res. Not. (IMRN)
Year: 2017


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.

Keywords: Geometric PDEs, Sinh-Gordon equation, Toda system, Blow up analysis, Boundary blow up