Abstract In this paper, we study the stability of k-Hessian overdetermined problems under small perturbations in R 2 {R^{2}} . Additionally, we give a proof for k-Hessian partially overdetermined problems and the related stability problems in R 2 {R^{2}} . The proof mainly replies to choosing a suitable auxiliary f.

中文翻译：

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平面域中k-Hessian超定和部分超定问题的稳定性

摘要 在本文中，我们研究了 R 2 {R^{2}} 中小扰动下 k-Hessian 超定问题的稳定性。此外，我们给出了 R 2 {R^{2}} 中 k-Hessian 部分超定问题和相关稳定性问题的证明。证明主要回答选择一个合适的辅助f。