Interior Schauder estimates for the fourth order Hamiltonian stationary equation in two dimensions
Arunima Bhattacharya, Micah Warren
TL;DR
This paper proves that solutions to the Hamiltonian stationary equation in two dimensions, which are initially $C^{1,1}$, are actually smooth and satisfy a $C^{2,eta}$ estimate, advancing regularity theory for this class of equations.
Contribution
It establishes interior regularity results for the Hamiltonian stationary equation in two dimensions, showing $C^{1,1}$ solutions are smooth and providing a $C^{2,eta}$ estimate.
Findings
Solutions that are $C^{1,1}$ are smooth.
A $C^{2,eta}$ estimate is derived for solutions.
Regularity results hold for all phases in two dimensions.
Abstract
We consider the Hamiltonian stationary equation for all phases in dimension two. We show that solutions that are will be smooth and we also derive a estimate for it.
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