Unique continuation for ∂ with square-integrable potentials

2022/03/08 by Pan, Yifei, Zhang, Yuan
#35A02 #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Primary 32W05 #Secondary 35A23

paper · doi:10.48550/arxiv.2203.04346

Abstract

In this paper, we investigate the unique continuation property for the inequality |∂ u| ≤ V|u|, where u is a vector-valued function from a domain in \mathbb Cⁿ to \mathbb C^N, and the potential V∈ L². We show that the strong unique continuation property holds when n=1, and the weak unique continuation property holds when n≥ 2. In both cases, the L² integrability condition on the potential is optimal.

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