Calculus of Variations and Geometric Measure Theory

W. Ao - A. Jevnikar - W. Yang

Blow up solutions for Sinh-Gordon equation with residual mass

created by jevnikar on 16 Dec 2019
modified on 17 Aug 2022


Accepted Paper

Inserted: 16 dec 2019
Last Updated: 17 aug 2022

Journal: Calc. Var. and PDEs
Year: 2022


We are concerned with the Sinh-Gordon equation in bounded domains. We construct blow up solutions with residual mass exhibiting either partial or asymmetric blow up, i.e. where both the positive and negative part of the solution blow up. This is the first result concerning residual mass for the Sinh-Gordon equation showing in particular that the concentration-compactness theory with vanishing residuals of Brezis-Merle can not be extended to this class of problems.

Keywords: Sinh-Gordon equation, Blow up analysis, residual mass, finite-dimensional reduction