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

Bhattacharya, Arunima; Warren, Micah

doi:10.1090/proc/14484

Interior Schauder estimates for the fourth order Hamiltonian stationary equation in two dimensions
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by Arunima Bhattacharya and Micah Warren PDF

Proc. Amer. Math. Soc. 147 (2019), 3471-3477 Request permission

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.

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