Convex domains and unique continuation at the boundary
Vilhelm AdolfssonChalmers University of Technology, Gothenburg, Sweden
Luis EscauriazaUniversidad del Pais Vasco, Bilbao, Spain
Carlos E. KenigUniversity 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.
Cite this article
Vilhelm Adolfsson, Luis Escauriaza, Carlos E. Kenig, Convex domains and unique continuation at the boundary. Rev. Mat. Iberoam. 11 (1995), no. 3, pp. 513–525DOI 10.4171/RMI/182