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


Authors: Arunima Bhattacharya and Micah Warren
Journal: Proc. Amer. Math. Soc. 147 (2019), 3471-3477
MSC (2010): Primary 35J30; Secondary 35J60
DOI: https://doi.org/10.1090/proc/14484
Published electronically: March 26, 2019
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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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Additional Information

Arunima Bhattacharya
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403–1222

Micah Warren
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403–1222

DOI: https://doi.org/10.1090/proc/14484
Received by editor(s): June 22, 2018
Received by editor(s) in revised form: November 28, 2018
Published electronically: March 26, 2019
Communicated by: Jiaping Wang
Article copyright: © Copyright 2019 American Mathematical Society