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Volume 29, Issue 3
A Pohožaev Identity and Critical Exponents of Some Complex Hessian Equations

Chi Li

J. Part. Diff. Eq., 29 (2016), pp. 175-194.

Published online: 2016-09

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  • 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.
  • Keywords

Pohožaev identity critical exponents complex Hessian equations

  • AMS Subject Headings

35J15, 35J60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

li2285@purdue.edu (Chi Li)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-29-175, author = {Chi and Li and li2285@purdue.edu and 4369 and Mathematics Department, Stony Brook University, Stony Brook NY, 11794-3651, USA and Chi Li}, title = {A Pohožaev Identity and Critical Exponents of Some Complex Hessian Equations}, journal = {Journal of Partial Differential Equations}, year = {2016}, volume = {29}, number = {3}, pages = {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.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v29.n3.2}, url = {http://global-sci.org/intro/article_detail/jpde/5087.html} }
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.
Chi Li. (2019). A Pohožaev Identity and Critical Exponents of Some Complex Hessian Equations. Journal of Partial Differential Equations. 29 (3). 175-194. doi:10.4208/jpde.v29.n3.2
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