Blow up solutions for Sinh-Gordon equation with residual mass

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...

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Veröffentlicht in:Calculus of variations and partial differential equations 2022-12, Vol.61 (6), Article 209
Hauptverfasser: Ao, Weiwei, Jevnikar, Aleks, Yang, Wen
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-022-02317-1