Inserted: 24 oct 2016
Last Updated: 4 dec 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