TY - JOUR
T1 - A Pohožaev Identity and Critical Exponents of Some Complex Hessian Equations
AU - Li , Chi
JO - Journal of Partial Differential Equations
VL - 3
SP - 175
EP - 194
PY - 2016
DA - 2016/09
SN - 29
DO - http://doi.org/10.4208/jpde.v29.n3.2
UR - https://global-sci.org/intro/article_detail/jpde/5087.html
KW - Pohožaev identity
KW - critical exponents
KW - complex Hessian equations
AB -  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.