Singular solutions to special Lagrangian equations with subcritical phases and minimal surface systems

By Dake Wang, Yu Yuan. 2011

58 citations recorded by the source corpus.

We construct singular solutions to special Lagrangian equations with subcritical phases and minimal surface systems. A priori estimate breaking families of smooth solutions are also produced correspondingly. A priori estimates for special Lagrangian equations with certain convexity are largely known by now.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/3b33320b599cf0cd8a5ae7a1ec394ea3f521ae8f

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In Applied Mathematics

1. Dake Wang
2. Edgard A. Pimentel
3. Yu Yuan
4. E. Teixeira
5. Micah W. Warren
6. Sebastien Picard
7. Tristan C. Collins
8. Xuan Wu

In Geometry and Topology

1. Dake Wang
2. Yu Yuan
3. E. Teixeira

Citations in the corpus

• Sharp hessian integrability estimates for nonlinear elliptic equations: an asymptotic approach (2015, background): “pend on the regularity of the hessian of u. It is known that the level set of (6) are convex if and only if |Θ| ≥ (d − 2)π/2, see [31]. When d = 3 and |Θ| < π/2, given any δ > 0, the authors in [30] build up solutions to (6) that are not in C1,δ. While the special Lagrangian equation is not un”
• Hessian estimates for special Lagrangian equations with critical and supercritical phases in general dimensions (2011, methodology): “ar. Partial Differential Equations 11(2000), 1–31. [U3] Urbas, John, An interior second derivative bound for solutions of Hessian equations. Calc. Var. Partial Differential Equations 12(2001), 417–431. [WdY] Wang, Dake and Yuan, Yu, Singular solutions to special Lagrangian equations with subcritical p”