Convex domains and unique continuation at the boundary
Vilhelm Adolfsson, Luis Escauriaza, Carlos E. Kenig · Revista Matemática Iberoamericana · 1995
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.