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On the backward uniqueness property for the heat equation in two-dimensional conical domains

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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 (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 \({95^{\circ}}\). 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 \({90^{\circ}}\).

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX26GG, Great Britain, UK

    Angkana Rüland

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  1. Angkana Rüland
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Correspondence to Angkana Rüland.

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This work is part of the Ph.D. thesis of the author written under the supervision of Prof. Dr. Herbert Koch to whom she owes great gratitude for his persistent support and advice. She thanks the Deutsche Telekom Stiftung and the Hausdorff Center for Mathematics for financial support.

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Rüland, A. On the backward uniqueness property for the heat equation in two-dimensional conical domains. manuscripta math. 147, 415–436 (2015). https://doi.org/10.1007/s00229-015-0764-4

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  • DOI: https://doi.org/10.1007/s00229-015-0764-4

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