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SUMMARY:Xavier Tolsa (Autonomous University of Barcelona)
DTSTART:20200709T130000Z
DTEND:20200709T135000Z
DTSTAMP:20260423T052547Z
UID:IMS/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IMS/37/">Uni
 que continuation at the boundary for harmonic functions</a>\nby Xavier Tol
 sa (Autonomous University of Barcelona) as part of PDE seminar via Zoom\n\
 n\nAbstract\nIn a work from 1991 Fang-Hua Lin asked the following question
 . Let $\\Omega\\subset\\mathbb R^n$ be a Lipschitz domain. Let $u$ be a fu
 nction harmonic in $\\Omega$ and continuous in $\\overline \\Omega$ which 
 vanishes et $\\Sigma \\subset \\partial\\Omega$ and moreover assume that t
 he normal derivative $\\partial_\\nu u$ vanishes in a subset of $\\Sigma$ 
 with positive surface measure. Is it true that then $u$ is identically zer
 o? \n\nUp to now\, the answer was known to be positive for $C^1$-Dini doma
 ins\, by results of Adolfsson-Escauriaza (1997) and Kukavica-Nystrom (1998
 ). In this talk I will explain a recent work where I show that the result 
 also holds for Lipschitz domains with small Lipschitz constant\, and thus 
 in particular for general $C^1$ domains.\n
LOCATION:https://researchseminars.org/talk/IMS/37/
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