Arunima Bhattacharya

activity

20172026

most citedHessian Estimates for Lagrangian mean curvature equation

17 citations · 49 across the 24 of their papers we have counts for

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18 papers · 1 filter

math.AP2026

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…

math.AP2025

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…

math.AP2025

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 $C^{n}$ . We prove that such a graph is smooth whenever its H…

math.AP2025

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., $∣Θ∣ \geq (n - 2) \frac{π}{2}$ , and extend our resul…

math.AP2025

Regularity for Hamiltonian stationary equations in $R_{n \leq 4}^{n}$

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 $n \leq 4$ , for all values of the L…

math.AP2024★ 1 cited

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…

math.AP2024

Hessian estimates for shrinkers, expanders, translators, and rotators of the Lagrangian Mean Curvature Flow

Arunima Bhattacharya, Jeremy Wall

In this paper, we prove interior Hessian estimates for shrinkers, expanders, translators, and rotators of the Lagrangian mean curvature flow under the assumption that the Lagrangia…

math.AP2023

Variational integrals on Hessian spaces: partial regularity for critical points

Arunima Bhattacharya, Anna Skorobogatova

We develop regularity theory for critical points of variational integrals defined on Hessian spaces of functions on open, bounded subdomains of $R^{n}$ , under compactly supp…

math.AP2022

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

Arunima Bhattacharya, Connor Mooney, Ravi Shankar

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…

math.AP2021★ 8 cited

A note on the two dimensional Lagrangian mean curvature equation

Arunima Bhattacharya

In this note, we use Warren-Yuan's super isoperimetric inequality on the level sets of subharmonic functions, which is available only in two dimensions, to derive a modified Hessia…

math.AP2021

Regularity for critical points of convex functionals on Hessian spaces

Arunima Bhattacharya

We consider variational integrals of the form $\int F (D^{2} u)$ where $F$ is convex and smooth on the Hessian space. We show that a critical point $u \in W^{2, \infty}$ of such a functi…

math.AP2020★ 1 cited

Optimal regularity for Lagrangian mean curvature type equations

Arunima Bhattacharya, Ravi Shankar

We classify regularity for Lagrangian mean curvature type equations, which include the potential equation for prescribed Lagrangian mean curvature and those for Lagrangian mean cur…

math.AP2020

Regularity for convex viscosity solutions of Lagrangian mean curvature equation

Arunima Bhattacharya, Ravi Shankar

We show that convex viscosity solutions of the Lagrangian mean curvature equation are regular if the Lagrangian phase has Hölder continuous second derivatives.

math.AP2020★ 17 cited

Hessian Estimates for Lagrangian mean curvature equation

Arunima Bhattacharya

In this paper, we derive a priori interior Hessian estimates for Lagrangian mean curvature equation if the Lagrangian phase is supercritical and has bounded second derivatives.

math.AP2020★ 9 cited

The Dirichlet problem for Lagrangian mean curvature equation

Arunima Bhattacharya

In this paper, we solve the Dirichlet problem with continuous boundary data for the Lagrangian mean curvature equation on a uniformly convex, bounded domain in $R^{n}$ .

math.AP2019★ 4 cited

$C^{2, α}$ estimates for solutions to almost linear elliptic equations

Arunima Bhattacharya, Micah Warren

In this paper, we show $C^{2, α}$ interior estimates for viscosity solutions of fully non-linear, uniformly elliptic equations, which are close to linear equations and we also compu…

math.AP2018★ 3 cited

Interior Schauder estimates for the fourth order Hamiltonian stationary equation in two dimensions

Arunima Bhattacharya, Micah Warren

We consider the Hamiltonian stationary equation for all phases in dimension two. We show that solutions that are $C^{1, 1}$ will be smooth and we also derive a $C^{2, α}$ estimate fo…

math.AP2017★ 5 cited

Regularity Bootstrapping For Fourth Order Non Linear Elliptic Equations

Arunima Bhattacharya, Micah Warren

We consider nonlinear fourth order elliptic equations of double divergence type. We show that for a certain class of equations where the nonlinearity is in the Hessian, solutions t…

Nonuniqueness of solutions to the Lagrangian mean curvature equation

Doubling and the two-dimensional critical valued Lagrangian phase

Optimal Regularity for Hölder continuous Hamiltonian Stationary Lagrangian graphs

Singularities of the Lagrangian mean curvature flow at the critical Lagrangian phase

Regularity for Hamiltonian stationary equations in Rn≤4n​

A Priori Estimates for Singularities of the Lagrangian Mean Curvature Flow with Supercritical Phase

Hessian estimates for shrinkers, expanders, translators, and rotators of the Lagrangian Mean Curvature Flow

Variational integrals on Hessian spaces: partial regularity for critical points

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

A note on the two dimensional Lagrangian mean curvature equation

Regularity for critical points of convex functionals on Hessian spaces

Optimal regularity for Lagrangian mean curvature type equations

Regularity for convex viscosity solutions of Lagrangian mean curvature equation

Hessian Estimates for Lagrangian mean curvature equation

The Dirichlet problem for Lagrangian mean curvature equation

C2,α estimates for solutions to almost linear elliptic equations

Interior Schauder estimates for the fourth order Hamiltonian stationary equation in two dimensions

Regularity Bootstrapping For Fourth Order Non Linear Elliptic Equations

Regularity for Hamiltonian stationary equations in $R_{n \leq 4}^{n}$

$C^{2, α}$ estimates for solutions to almost linear elliptic equations