Volume 55, Issue 1
Gradient Bounds for Almost Complex Special Lagrangian Equation with Supercritical Phase

J. Math. Study, 55 (2022), pp. 71-83.

Published online: 2022-01

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• Abstract

In this article, we will consider the Dirichlet problem for special Lagrangian equation on $\Omega\subset M$, where $(M,J)$ is a compact almost complex manifold. Under the existence of $C^{2}$-smooth strictly $J$-plurisubharmonic subsolution $\underline{u}$, in the supercritical phase case, we  obtain a uniform global gradient estimate.

• Keywords

Special Lagrangian equation, almost complex manifold, gradient estimates, maximum principle.

53C07, 32Q60, 35B50

zjgmath@mail.ustc.edu.cn (Jiaogen Zhang)

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@Article{JMS-55-71, author = {Jiaogen and Zhang and zjgmath@mail.ustc.edu.cn and 22008 and School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China and Jiaogen Zhang}, title = {Gradient Bounds for Almost Complex Special Lagrangian Equation with Supercritical Phase}, journal = {Journal of Mathematical Study}, year = {2022}, volume = {55}, number = {1}, pages = {71--83}, abstract = {

In this article, we will consider the Dirichlet problem for special Lagrangian equation on $\Omega\subset M$, where $(M,J)$ is a compact almost complex manifold. Under the existence of $C^{2}$-smooth strictly $J$-plurisubharmonic subsolution $\underline{u}$, in the supercritical phase case, we  obtain a uniform global gradient estimate.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v55n1.22.06}, url = {http://global-sci.org/intro/article_detail/jms/20195.html} }
TY - JOUR T1 - Gradient Bounds for Almost Complex Special Lagrangian Equation with Supercritical Phase AU - Zhang , Jiaogen JO - Journal of Mathematical Study VL - 1 SP - 71 EP - 83 PY - 2022 DA - 2022/01 SN - 55 DO - http://doi.org/10.4208/jms.v55n1.22.06 UR - https://global-sci.org/intro/article_detail/jms/20195.html KW - Special Lagrangian equation, almost complex manifold, gradient estimates, maximum principle. AB -

In this article, we will consider the Dirichlet problem for special Lagrangian equation on $\Omega\subset M$, where $(M,J)$ is a compact almost complex manifold. Under the existence of $C^{2}$-smooth strictly $J$-plurisubharmonic subsolution $\underline{u}$, in the supercritical phase case, we  obtain a uniform global gradient estimate.

Jiaogen Zhang. (2022). Gradient Bounds for Almost Complex Special Lagrangian Equation with Supercritical Phase. Journal of Mathematical Study. 55 (1). 71-83. doi:10.4208/jms.v55n1.22.06
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