Radial solutions of a fourth order Hamiltonian stationary equation
Analysis of PDEs
2016-12-12 v1 Differential Geometry
Abstract
We consider smooth radial solutions to the Hamiltonian stationary equation which are defined away from the origin. We show that in dimension two all radial solutions on unbounded domains must be special Lagrangian. In contrast, for all higher dimensions there exist non-special Lagrangian radial solutions over unbounded domains; moreover, near the origin, the gradient graph of such a solution is continuous if and only if the graph is special Lagrangian.
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Cite
@article{arxiv.1612.02852,
title = {Radial solutions of a fourth order Hamiltonian stationary equation},
author = {Jingyi Chen and Micah Warren},
journal= {arXiv preprint arXiv:1612.02852},
year = {2016}
}
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17 pages