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arXiv · 2501.04254

Solutions of the Special Lagrangian Equation near Infinity

Qing Han·Ilya Marchenko
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Abstract

Solutions to special Lagrangian equations near infinity, with supercritical phases or with semiconvexity on solutions, are known to be asymptotic to quadratic polynomials for dimension $n\ge 3$, with an extra logarithmic term for $n=2$. Via modified Kelvin transforms, we characterize remainders in the asymptotic expansions by a single function near the origin. Such a function is smooth in even dimension, but only $C^{n-1,\alpha}$ in odd dimension $n$, for any $\alpha\in (0,1)$.

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Qing Han, Ilya Marchenko. 2025-01-08. Solutions of the Special Lagrangian Equation near Infinity. https://arxiv.org/abs/2501.04254

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