Convex domains and unique continuation at the boundary

  • Vilhelm Adolfsson

    Chalmers University of Technology, Gothenburg, Sweden
  • Luis Escauriaza

    Universidad del Pais Vasco, Bilbao, Spain
  • Carlos E. Kenig

    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.

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. 513–525

DOI 10.4171/RMI/182