Work

Gradient estimates for the Lagrangian mean curvature equation with critical and supercritical phase

Year: 2026

Type: article

Abstract: : In this paper, we prove interior gradient estimates for the Lagrangian mean curvature equation, if the Lagrangian phase is critical and supercritical and $C^2$. Combined with the a priori interior Hessian estimates proved by the first author, this solves the Dirichlet boundary value problem for the critical and supercritical Lagrangian mean curvature equation with $C^0$ boundary data. We also provide a uniform gradient estimate for lower regularity phases that satisfy certain additional hypotheses.

Source: American Journal of Mathematics

DOI: 10.1353/ajm.2026.a991626

Authors: Arunima Bhattacharya, Connor Mooney, Ravi Shankar

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4281658755

FWCI:

Cites:

Cited by: 2

Related to: 10