https://scholars.lib.ntu.edu.tw/handle/123456789/626579
標題: | Improved quantitative unique continuation for complex-valued drift equations in the plane | 作者: | Davey, B Kenig, C JENN-NAN WANG |
關鍵字: | Carleman estimates; elliptic systems; quantitative unique continuation; 2ND-ORDER ELLIPTIC-EQUATIONS; LANDIS CONJECTURE; NODAL SETS; EIGENFUNCTIONS | 公開日期: | 1-十一月-2022 | 出版社: | WALTER DE GRUYTER GMBH | 卷: | 34 | 期: | 6 | 起(迄)頁: | 1641 | 來源出版物: | FORUM MATHEMATICUM | 摘要: | In this article, we investigate the quantitative unique continuation properties of complex-valued solutions to drift equations in the plane. We consider equations of the form Δu + W · ∇u = 0 in ℝ2, where W = W1 + iW2 with each Wj being real-valued. Under the assumptions that Wj ∈ Lqj for some q1 ∈ [2, ∞], q2 ∈ [2, ∞] and that W2 exhibits rapid decay at infinity, we prove new global unique continuation estimates. This improvement is accomplished by reducing our equations to vector-valued Beltrami systems. Our results rely on a novel order of vanishing estimate combined with a finite iteration scheme. |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/626579 | ISSN: | 0933-7741 | DOI: | 10.1515/forum-2022-0114 |
顯示於: | 應用數學科學研究所 |
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