Annali di Matematica Pura ed Applicata (1923 -)

, Volume 195, Issue 4, pp 1123–1151 | Cite as

Critical blowup exponent to a class of semilinear elliptic equations with constraints in higher dimension-local properties

  • Takashi Suzuki
  • Ryo TakahashiEmail author


We study a class of semilinear elliptic equations with constraints in higher dimension. It is known that several mathematical structures of the problem are closed to those of the Liouville equation in dimension two. In this paper, we establish a classification of entire solutions, the sup \(+\) inf-type inequality and the quantized blowup mechanism.


Critical blowup exponent Scaling invariance Classification of entire solutions sup \(+\) inf-type inequality Blowup Quantization 

Mathematics Subject Classification

35B33 35J61 35A20 35B08 35Q60 



This work is partially supported by Scientific Research A (No. 26247013) of Japan Society for the Promotion of Science (JSPS).


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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Division of Mathematical Science, Department of Systems Innovation, Graduate School of Engineering ScienceOsaka UniversityToyonakashiJapan

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