二维外域椭圆方程解的渐近行为
偏微分方程分析
2026-05-14 v3
摘要
研究二阶椭圆方程在外域中的渐近行为。在解属于 Lorentz 空间 或弱 Lebesgue 空间 的情况下，给出解在空间无穷远处的自然且接近尖锐的点估计。该证明基于 Korobkov--Pileckas--Russo [4] 的论证方法，其中研究了二维 Navier--Stokes 方程湍流方程解的衰减性质。
关键词
引用
@article{arxiv.2406.12245,
title = {Asymptotic behavior of solutions to elliptic equations in 2D exterior domains},
author = {Hideo Kozono and Yutaka Terasawa and Yuta Wakasugi},
journal= {arXiv preprint arXiv:2406.12245},
year = {2026}
}
备注
Proposition 2.2 is added, and the geometry of level sets of solution is analyzed more precisely. Also, Section 2.3 is added, and the derivation of Theorem 1.1 from Lemma 2.3 is revised. 13 pages, 3 figures