On the strong unique continuation property for the Dirac operator

2025/05/06 by Biagio Cassano, Cassano, Biagio
Computer Science · Mathematics · #35B60 #35B99 #35Q40 #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2505.03421

openalex publication_date 2025/05/06 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

In [DO99,KY99], the strong unique continuation property from the origin is established for H_loc¹-solutions to the massless Dirac differential inequality |D_n u | ≤ (C)/(|x|)|u|, in dimension n≥ 2 and with C<\frac12. We show that \frac12 is the largest possibile constant in this result, providing an example in ℝ² of a (non-trivial) solution of the inequality. Also, we show properties of unique continuation from the origin for solutions to the inequality |D_n u | ≤ (C)/( |x|^γ)|u|, for γ>1, C>0. Finally, we establish the strong unique continuation property for the Dirac operator from the point at infinity.

Citations

• Carleman estimates and boundedness of associated multiplier operators
• Unique continuation for fractional Schrödinger operators in three and higher dimensions
• Carleman estimates and inverse problems for Dirac operators

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• Resolvent estimates of the Dirac operator
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