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The Neumann problem for a class of complex Hessian quotient equations

Yuying Qian|Qiang Tu|Chenyue Xue
대한수학회 (The Korean Mathematical Society)|2024.07|대한수학회보 (Bulletin of the KMS)|제61권 제4호|pp. 999-1017|DOI 10.4134/BKMS.b230565

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참고문헌

키워드

Hessian quotient equationNeumann problema priori estimates
주제분류수학

초록

In this paper, we study the Neumann problem for the complex Hessian quotient equation $\frac{\sigma_k(\tau\Delta uI+\partial\bar{\partial} u)}{\sigma_l(\tau\Delta uI+\partial\bar{\partial} u)}=\psi$ with $0\leq l<k\leq n$. We prove a priori estimate and global $C^1$ estimates, in particular, we use the double normal second derivatives on the boundary to establish the global $C^2$ estimates and prove the existence and the uniqueness for the Neumann problem of the above complex Hessian quotient equation.

Abstract

In this paper, we study the Neumann problem for the complex Hessian quotient equation $\frac{\sigma_k(\tau\Delta uI+\partial\bar{\partial} u)}{\sigma_l(\tau\Delta uI+\partial\bar{\partial} u)}=\psi$ with $0\leq l<k\leq n$. We prove a priori estimate and global $C^1$ estimates, in particular, we use the double normal second derivatives on the boundary to establish the global $C^2$ estimates and prove the existence and the uniqueness for the Neumann problem of the above complex Hessian quotient equation.

참고문헌 (34)

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