8 papers · 1 filter
Nonuniqueness of solutions to the Lagrangian mean curvature equation
Arunima Bhattacharya, W. Jacob Ogden
We resolve a question posed by Harvey and Lawson concerning the uniqueness of continuous viscosity solutions to the Dirichlet problem for the Lagrangian mean curvature equation on…
Doubling and the two-dimensional critical valued Lagrangian phase
Arunima Bhattacharya, Ravi Shankar, Jeremy Wall
In this paper, we establish interior Hessian and gradient estimates for the two-dimensional Lagrangian mean curvature equation when the phase changes signs, provided the gradient o…
Optimal Regularity for Hölder continuous Hamiltonian Stationary Lagrangian graphs
Arunima Bhattacharya, W. Jacob Ogden
In this paper, we establish optimal regularity for Hölder continuous Hamiltonian stationary Lagrangian graphs in . We prove that such a graph is smooth whenever its…
Singularities of the Lagrangian mean curvature flow at the critical Lagrangian phase
Arunima Bhattacharya, Ravi Shankar, Jeremy Wall +1
We establish interior estimates for singularities of the Lagrangian mean curvature flow when the Lagrangian phase is critical, i.e., , and extend our res…
Regularity for Hamiltonian stationary equations in
Arunima Bhattacharya
In this paper, we study the regularity of solutions to the Hamiltonian stationary equation in complex Euclidean space. We show that in dimensions , for all values of the L…
A Priori Estimates for Singularities of the Lagrangian Mean Curvature Flow with Supercritical Phase
Arunima Bhattacharya, Jeremy Wall
In this paper, we prove interior a priori estimates for singularities of the Lagrangian mean curvature flow assuming the Lagrangian phase is supercritical. We prove a Jacobi inequa…