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

Abstract

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 $C^{2,\alpha }$ estimate for it.

References in corpus (2)

• A Bernstein problem for special Lagrangian equations
• Concavity of the Lagrangian Phase Operator and Applications