论文标题
Sobolev型超临界K-Hessian不平等的极端功能
Extremal functions for a supercritical k-Hessian inequality of Sobolev-type
论文作者
论文摘要
本文中我们的主要目的是调查$ k $ -Hessian操作员的超批评性sobolev-type不平等，该操作员在$φ^{k} _ {0，\ mathrm {rad}}（b）$上，radyally symmetric $ k $ k $ k $ - admissible在单位球$ b \ subset $ b \ subset $ bb b \ subset $ bb b b s sset}我们还证明了与超临界增长相关的$ k $ -Hessian方程的相关变异问题的可允许的极端功能的存在。
Our main purpose in this paper is to investigate a supercritical Sobolev-type inequality for the $k$-Hessian operator acting on $Φ^{k}_{0,\mathrm{rad}}(B)$, the space of radially symmetric $k$-admissible functions on the unit ball $B\subset\mathbb{R}^{N}$. We also prove both the existence of admissible extremal functions for the associated variational problem and the solvability of a related $k$-Hessian equation with supercritical growth.
