Davey, BBDaveyKenig, CCKenigJENN-NAN WANG2022-12-192022-12-192022-11-010933-7741https://scholars.lib.ntu.edu.tw/handle/123456789/626579In 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.Carleman estimates; elliptic systems; quantitative unique continuation; 2ND-ORDER ELLIPTIC-EQUATIONS; LANDIS CONJECTURE; NODAL SETS; EIGENFUNCTIONSjournal article10.1515/forum-2022-01142-s2.0-85133880291WOS:000818114600001https://api.elsevier.com/content/abstract/scopus_id/85133880291