Revista Matemática Iberoamericana
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Published online: 1995-12-31
Convex domains and unique continuation at the boundaryVilhelm Adolfsson, Luis Escauriaza and Carlos E. Kenig (1) Chalmers University of Technology, Gothenburg, Sweden
(2) Universidad del Pais Vasco, Bilbao, Spain
(3) University of Chicago, USA
We show that a harmonic function which vanishes continuously on an open set of the boundary of a convex domain cannot have a normal derivative which vanishes on a subset of positive surface measure. We also prove a similar result for caloric functions vanishing on the lateral boundary of a convex cylinder.
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Adolfsson Vilhelm, Escauriaza Luis, Kenig Carlos: Convex domains and unique continuation at the boundary. Rev. Mat. Iberoam. 11 (1995), 513-525. doi: 10.4171/RMI/182