Revista Matemática Iberoamericana

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Volume 11, Issue 3, 1995, pp. 513–525
DOI: 10.4171/RMI/182

Published online: 1995-12-31

Convex domains and unique continuation at the boundary

Vilhelm Adolfsson[1], Luis Escauriaza[2] and Carlos E. Kenig[3]

(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