The complex Hessian equation with infinite Dirichlet boundary value

Xiang, Ni; Yang, Xiao-Ping

doi:10.1090/S0002-9939-08-09354-4

The complex Hessian equation with infinite Dirichlet boundary value
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by Ni Xiang and Xiao-Ping Yang PDF

Proc. Amer. Math. Soc. 136 (2008), 2103-2111 Request permission

Abstract:

The existence and nonexistence of the $\Gamma$-subharmonic solutions for the complex Hessian equations with infinite Dirichlet boundary value are proved in the certain bounded domain in $C^n$. We calculate the k-Hessian of the radially symmetric function and use radial functions to construct various barrier functions in this paper. Moreover, it is shown that the growth rate conditions are nearly optimal.

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Ni Xiang and Xiao-Ping Yang, The complex Monge-Ampère equation with infinite Dirichlet boundary value, Nonlinear Analysis, to appear.