论文标题
K-Hessian方程的半径向溶液的表征
A characterization of semistable radial solutions of k-Hessian equations
论文作者
论文摘要
我们表征了方程式的半径向解决方案$ s_k \ left（d^2u \ right）= g（u）\; \ mbox {in} b_1 $，其中$ b_1 $是$ \ mathbb {r}^n $，$ d^2u $的单位球， $ s_k \ left（d^2u \ right）$表示$ u $的$ k $ -Hessian运营商。作者最近在[8]中引入了这类径向解决方案。这些证明是相对于[8]中给出的新的，并关注方程的结构，从而改善了一些先前的结果。
We characterize semistable radial solutions of the equation $S_k\left(D^2u\right)=g(u)\;\mbox{in } B_1$, where $B_1$ is the unit ball of $\mathbb{R}^n$, $D^2u$ is the Hessian matrix of $u,\,g$ is a positive $C^1$ nonlinearity and $S_k\left(D^2u\right)$ denotes the $k$-Hessian operator of $u$. This class of radial solutions has been recently introduced by the authors in [8]. The proofs are new relative to those given in [8] and focus on the structure of the equation directly, thereby improving some previous results.
