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<p>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.</p>

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Interior and Boundary Unique Continuation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月30日

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  • Carlos E. Kenig,
  • Zihui Zhao

摘要

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.