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May 6, 2026La Matematica0 citationsOpen Access

Interior and Boundary Unique Continuation

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CKCarlos E. KenigZZZihui Zhao

Key Points

  • This article explores unique continuation results for elliptic equations, both at the interior and boundary.
  • Reviewed classical results of interior unique continuation.
  • Described boundary unique continuation results.
  • Examined connections with geometric problems regarding nodal, singular, and critical sets.
  • Found unique continuation properties for elliptic equations.
  • Discussed implications on sets in both the interior and boundary.
  • Highlighted connections with low regularity assumptions.

Abstract

Abstract In this expository article we describe classical interior unique continuation results, and boundary unique continuation results, for elliptic equations. We also describe connections with geometric problems dealing with nodal sets, singular sets and critical sets, both in the interior and at the boundary, on domains with low regularity assumptions on the normal direction.

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Cite This Study

Kenig et al. (2026) studied this question.

synapsesocial.com/papers/69fa98bd04f884e66b5328f8https://doi.org/10.1007/s44007-026-00218-9
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