On the backward uniqueness property for the heat equation in two-dimensional conical domains - Rüland, Angkana (Manuscripta mathematica, 2015)
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 (Commun. Partial Differ. Equ. 37(8):1414-1429, 2012) on the minimal angle in which the backward uniqueness property is displayed: We reach angles of slightly less than $${95^{°}}$$. 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 $${90^{°}}$$.
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