On the Dirichlet problem for Lagrangian phase equation with critical and supercritical phase

2022/04/11 by Lu, Siyuan · 3 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2204.05420

Abstract

In this paper, we solve the Dirichlet problem for Lagrangian phase equation with critical and supercritical phase. A crucial ingredient is the interior C² estimate. Our result is sharp in the sense that there exist singular solutions in the subcritical phase case.

Cited by

• Boundary estimates for a fully nonlinear Yamabe problem on Riemannian manifolds
• Doubling and the two-dimensional critical valued Lagrangian phase
• Singularities of the Lagrangian mean curvature flow at the critical Lagrangian phase

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