Asymptotic behavior of solutions to elliptic equations in 2D exterior domains
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911677731045376 |
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| author | Kozono, Hideo Terasawa, Yutaka Wakasugi, Yuta |
| author_facet | Kozono, Hideo Terasawa, Yutaka Wakasugi, Yuta |
| contents | 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 $L^{p,q}$ or the weak Lebesgue space $L^{p,\infty}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12245 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic behavior of solutions to elliptic equations in 2D exterior domains Kozono, Hideo Terasawa, Yutaka Wakasugi, Yuta Analysis of PDEs 35J15, 35K10, 35B53 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 $L^{p,q}$ or the weak Lebesgue space $L^{p,\infty}$ 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. |
| title | Asymptotic behavior of solutions to elliptic equations in 2D exterior domains |
| topic | Analysis of PDEs 35J15, 35K10, 35B53 |
| url | https://arxiv.org/abs/2406.12245 |