Solutions of the Special Lagrangian Equation near Infinity

Fuente: arXiv
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Main Authors: Han, Qing, Marchenko, Ilya
Format: Preprint
Published: 2025
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author Han, Qing
Marchenko, Ilya
author_facet Han, Qing
Marchenko, Ilya
contents 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 $C^{n-1,α}$ in odd dimension $n$, for any $α\in (0,1)$.
format Preprint
id arxiv_https___arxiv_org_abs_2501_04254
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Solutions of the Special Lagrangian Equation near Infinity
Han, Qing
Marchenko, Ilya
Analysis of PDEs
Differential Geometry
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 $C^{n-1,α}$ in odd dimension $n$, for any $α\in (0,1)$.
title Solutions of the Special Lagrangian Equation near Infinity
topic Analysis of PDEs
Differential Geometry
url https://arxiv.org/abs/2501.04254