Unique continuation on convex domains

• Sean McCurdy ^[1]
  1. [1] University of Washington

     University of Washington

     Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 1, 2023, págs. 1-28
• Idioma: inglés
• DOI: 10.4171/RMI/1389
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• Resumen

  • In this paper, we obtain estimates on the quantitative strata of the critical set of non-trivial harmonic functions u which vanish continuously on ⊂∂ΩV⊂∂Ω, a relatively open subset of the boundary of a convex domain Ω⊂Ω⊂Rn. In particular, these estimates improve dimensional estimates on {∣∇∣=0}{∣∇u∣=0} both in ⊂∂ΩV⊂∂Ω and as it approaches ∩Ω‾V∩Ω. 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.