Expository article describes unique continuation in elliptic equations, suggesting implications for geometric problems.
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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Kenig et al. (2026) studied this question.
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