Asymptotic behavior of solutions to elliptic equations in 2D exterior domains
Abstract
The asymptotic behavior of solutions to the second order elliptic equations in exterior domains is studied. In particular, under the assumption that the solution belongs to the Lorentz space or the weak Lebesgue space with certain conditions on the coefficients, we give natural and an almost sharp pointwise estimate of the solution at spacial infinity. The proof is based on the argument by Korobkov--Pileckas--Russo [4], in which the decay property of the solution to the vorticity equation of the two-dimensional Navier--Stokes equations was studied.
Cite
@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}
}
Comments
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