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arXiv · 2504.18013

Regularity for Hamiltonian stationary equations in $\mathbb{R}_{n\leq 4}^{n}$

Arunima Bhattacharya
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Abstract

In this paper, we study the regularity of solutions to the Hamiltonian stationary equation in complex Euclidean space. We show that in dimensions $n\leq 4$, for all values of the Lagrangian phase, any $C^{1,1}$ solution is smooth and derive a $C^{k,\alpha}$ estimate for it, where $k \geq 2$.

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Arunima Bhattacharya. 2025-04-25. Regularity for Hamiltonian stationary equations in $\mathbb{R}_{n\leq 4}^{n}$. https://arxiv.org/abs/2504.18013

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