Acta Mathematica Sinica, English Series

, Volume 34, Issue 4, pp 681–690 | Cite as

On a Conformally Invariant Integral Equation Involving Poisson Kernel



We study a prescribing functions problem of a conformally invariant integral equation involving Poisson kernel on the unit ball. This integral equation is not the dual of any standard type of PDE. As in Nirenberg problem, there exists a Kazdan–Warner type obstruction to existence of solutions. We prove existence in the antipodal symmetry functions class.


Poisson kernel conformal invariance blow up analysis 

MR(2010) Subject Classification

45G05 35B33 


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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical sciencesBeijing Normal UniversityBeijingP. R. China

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