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Espinar, Laurent Mazet","submitted_at":"2016-10-31T09:04:47Z","abstract_excerpt":"We show uniqueness for overdetermined elliptic problems defined on topological disks $\\Omega$ with $C^2$ boundary, i.e., positive solutions $u$ to $\\Delta u + f(u)=0$ in $\\Omega \\subset (M^2,g)$ so that $u = 0$ and $\\frac{\\partial u}{\\partial \\vec\\eta} = cte $ along $\\partial \\Omega$, $\\vec\\eta$ the unit outward normal along $\\partial\\Omega$ under the assumption of the existence of a candidate family. 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