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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
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 H…
math.AP2023
Remarks on the Complex Euler Equations
Dallas Albritton, W. Jacob Ogden
We consider a complexification of the Euler equations introduced by Šverák which conserves energy. We prove that these complex Euler equations are nonlinearly ill-posed below analy…