Classification of the Solutions to an Overdetermined Elliptic Problem in the Plane

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Solutions to overdetermined elliptic problems in nontrivial exterior domains (2016, background): “Partial positive answers to the BCN conjecture in dimension 2 have been given in several works, see [10, 13, 20, 21, 31, 33].”
Serrin’s overdetermined problem and constant mean curvature surfaces (2013, background): “2) is solvable for f = 0 is given by Traizet in [27].”
A Rigidity Result for Overdetermined Elliptic Problems in the Plane (2015, methodology): “This is done via a blowup argument, making use of the classification results of [34] for the case f D 0.”