Year: 2016
Author: Chi Li
Journal of Partial Differential Equations, Vol. 29 (2016), Iss. 3 : pp. 175–194
Abstract
In this paper, we prove some sharp non-existence results for Dirichlet problems of complex Hessian equations. In particular, we consider a complex Monge-Ampère equation which is a local version of the equation of Kähler-Einstein metric. The non-existence results are proved using the Pohožaev method. We also prove existence results for radially symmetric solutions. Themain difference of the complex case with the real case is that we don't know if a priori radially symmetric property holds in the complex case.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v29.n3.2
Journal of Partial Differential Equations, Vol. 29 (2016), Iss. 3 : pp. 175–194
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Pohožaev identity
Author Details
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Moser–Trudinger type inequalities for complex Monge–Ampère operators and Aubin’s “hypothèse fondamentale”
Berman, Robert J.
Berndtsson, Bo
Annales de la Faculté des sciences de Toulouse : Mathématiques, Vol. 31 (2022), Iss. 3 P.595
https://doi.org/10.5802/afst.1704 [Citations: 6]