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THE NEUMANN PROBLEM FOR A CLASS OF COMPLEX HESSIAN QUOTIENT EQUATIONS
THE NEUMANN PROBLEM FOR A CLASS OF COMPLEX HESSIAN QUOTIENT EQUATIONS
- 대한수학회
- Bulletin of the Korean Mathematical Society
- Vol.61No.4
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2024.01999 - 1017 (19 pages)
- 0
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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 ≤ 𝑙 < k ≤ n. We prove a priori estimate and global C<sup>1</sup> estimates, in particular, we use the double normal second derivatives on the boundary to establish the global C<sup>2</sup> estimates and prove the existence and the uniqueness for the Neumann problem of the above complex Hessian quotient equation.
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