Hessian and gradient estimates for three dimensional special Lagrangian equations with large phase

By Micah W. Warren, Yu Yuan. 2008

61 citations recorded by the source corpus.

We obtain a priori interior Hessian and gradient estimates for special Lagrangian equations with phase larger than a critical value in dimension three. Gradient estimates are also derived for critical and super critical phases in general dimensions.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1b8b224de9d5aba5ad06262ed8a3090d3c33b85a

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In Applied Mathematics

1. Dake Wang
2. Yu Yuan
3. Sebastien Picard
4. Tristan C. Collins
5. Xuan Wu
6. Micah W. Warren
7. Jingyi Chen
8. Chi Li

In Computational Theory and Mathematics

1. Dake Wang
2. Yu Yuan
3. Micah W. Warren
4. Jingyi Chen
5. Sebastien Picard
6. Tristan C. Collins
7. Xuan Wu

Citations in the corpus

• Hessian estimates for special Lagrangian equations with critical and supercritical phases in general dimensions (2011, background): “e. Comm. Pure Appl. Math. 62(2009), no. 3, 305–321. [WY3] Warren, Micah and Yuan, Yu, Explicit gradient estimates for minimal Lagrangian surfaces of dimension two. Math. Z. 262(2009), no. 4, 867–879. [WY4] Warren, Micah and Yuan, Yu, Hessian and gradient estimates for three dimensional special Lagra”
• A priori estimate for convex solutions to special Lagrangian equations and its application (2009, background): “1) Hessian estimates have been obtained: when the solutions are convex with small gradients in [19]; when n D 2 in [20] (giving a sharper bound than in [9]); when n D 3 and j‚j 2 , including the equation 2 D(2)u D 1 in dimension 3, in [21, 22].”
• Singular solutions to special Lagrangian equations with subcritical phases and minimal surface systems (2011, background): “oblem with smooth boundary data to the now convex special Lagrangian equation (1.1) in the critical and supercritical phase cases, the regularity of C0 viscosity solutions were derived in [WY1] [WY2] [WY3] [CWY]. In passing, we also mention that the existence and uniquenessof the C0 viscosity soluti”
• Concavity of the Lagrangian phase operator and applications (2016, methodology): “estimates for the minimal surface system were first established by M.-T. Wang in [36]. Interior estimates for the special Lagrangian equation with supercritical phase have been obtained by Warren-Yuan [38] for the C1 estimate and Wang-Yuan [33] for the C2 estimate. In [1], Brendle-Warren study a boun”