Hessian estimates for special Lagrangian equations with critical and supercritical phases in general dimensions

By Dake Wang, Yu Yuan. 2011

90 citations recorded by the source corpus.

We derive a priori interior Hessian estimates for special Lagrangian equation with critical and supercritical phases in general higher dimensions. Our unified approach leads to sharper estimates even for the previously known three dimensional and convex solution cases.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/be32abe5eab661ba364a7d5ba43ef7f6710cf1e2

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In Applied Mathematics

1. Tristan C. Collins
2. Sebastien Picard
3. Xuan Wu
4. Chi Li

In Mathematical Physics

1. Tristan C. Collins
2. Sebastien Picard
3. Xuan Wu

Citations in the corpus

• Concavity of the Lagrangian phase operator and applications (2016, methodology): “ome facts about functions with supercritical Lagrangian phase– namely, functions satisfying F(D2u) := X i arctan(λi) = h(x) with h(x) >(n−2)π 2. These properties are well-known and can be found in [33, 39]. Lemma 2.1. Suppose λ1 > λ2 > ··· > λn are such that P i arctanλi > (n− 2)π 2 +”