A priori estimates for solutions of fully nonlinear special lagrangian equations

By Yu Yuan. 2001

48 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a8db660495c5f337fb12d79c9b7d5efe16f8c9ab

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Partial regularity of solutions of fully nonlinear, uniformly elliptic equations (2011, background): “1) have also been shown to be classical solutions for certain classes of nonconvex operators by Yuan [11] as well as Cabré and Caffarelli [1].”
Plurisubharmonicity in a General Geometric Context (2008, background): “However, the smoothness of the solutions for smooth boundary data remains largely open (see [ Y ] however).”
A Bernstein problem for special Lagrangian equations (2002, methodology): “ proof. One can also take advantage of the special Lagrangian equation (1.1), use the compactness result for viscosity solution to derive that M v = (¯x,▽v(¯x)) is a minimal surface, see Lemma 2.2 in [Y]. Proposition 3.1. There exist a dimensional constant ε′ (n) > 0 such that any minimal surface”
Estimates in the generalized Campanato-John-Nirenberg spaces for fully nonlinear elliptic equations (2003, background): “cave and nonconvex equations (see [CY], [H2], [ Y ]).”
Singular solutions to special Lagrangian equations with subcritical phases and minimal surface systems (2011, background): “ guess that all C1,α for α > 1 3 solutions to special Lagrangian equation (1.1) with n = 3 should be regular (analytic). This regularity for C1,1 solutions to (1.1) in dimension three was shown in [Y1]. Earlier on, Urbas [U, Theorem 1.1] proved the regularity for better than Pogorelov solutions, ”
Elliptic PDE's in probability and geometry: Symmetry and regularity of solutions (2007, unknown): “It is still a major open problem to know if the hypothesis F concave (or convex) is needed in this theorem —see [12, 16, 53] for some results in this topic.”