Unique continuation on convex domains

  • Sean McCurdy

    University of Washington, Seattle, USA
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In this paper, we obtain estimates on the quantitative strata of the critical set of non-trivial harmonic functions which vanish continuously on , a relatively open subset of the boundary of a convex domain . In particular, these estimates improve dimensional estimates on both in and as it approaches . These estimates are not obtainable by naively combining interior and boundary estimates, and represent a significant improvement upon existing results for boundary analytic continuation in the convex case.

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Sean McCurdy, Unique continuation on convex domains. Rev. Mat. Iberoam. 39 (2023), no. 1, pp. 1–28

DOI 10.4171/RMI/1389