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

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.