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The Dirichlet problem of generalized special Lagrangian type equations and curvature version

Part of: Symplectic geometry, contact geometry Elliptic equations and systems

Published online by Cambridge University Press:  04 April 2025

Ni Xiang  and
Yuni Xiong
Ni Xiang
Affiliation:
Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, P.R. China e-mail: nixiang@hubu.edu.cn
Yuni Xiong*
Affiliation:
Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, P.R. China e-mail: nixiang@hubu.edu.cn
*
e-mail: 202121104011767@stu.hubu.edu.cn
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Abstract

This article focuses on two kinds of generalized special Lagrangian type equations. We investigate the Dirichlet problem for these equations with supercritical phase and critical phase in $\mathbb {R}^n$, deriving the a priori estimates and establishing the existence under the assumption of a subsolution. Furthermore, we also consider the corresponding special Lagrangian curvature type equations with supercritical phase and critical phase.

Keywords

Generalized special Lagrangian type equationsspecial Lagrangian curvature type equationsthe Dirichlet problem

MSC classification

Primary: 35J60: Nonlinear elliptic equations
Secondary: 53D12: Lagrangian submanifolds; Maslov index

Information

Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 27
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

This research was supported by funds from the National Natural Science Foundation of China No. 11971157, No. 12426532.

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