On the Backward Uniqueness Property for the Heat Equation in Two-Dimensional Conical Domains

Abstract

In this article we deal with the backward uniqueness property of the heat equation in conical domains in two spatial dimensions via Carleman inequality techniques. Using a microlocal interpretation of the pseudoconvexity condition, we improve the bounds of Šverák and Li on the minimal angle in which the backward uniqueness property is displayed: We reach angles of slightly less than $95^{\circ }$. Via two-dimensional limiting Carleman weights we obtain the uniqueness of possible controls of the heat equation with lower order perturbations in conical domains with opening angles larger than $90^{\circ }$

23 pages

References in corpus (4)

• Limiting Carleman weights and anisotropic inverse problems
• On the null-controllability of the heat equation in unbounded domains
• On Backward Uniqueness for the Heat Operator in Cones
• Backward uniqueness for the heat equation in cones