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Yifei Pan and
Yuan Zhang
Unique continuation for d-bar with square-integrable potentials
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| Published: |
March 23, 2023. |
| Keywords: |
Cauchy-Riemann equation, unique continuation, Hardy-Littlewood-Sobolev inequality. |
| Subject [2010]: |
Primary 32W05; Secondary 35A23, 35A02. |
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Abstract
In this paper, we investigate the unique continuation property for the inequality $|\bar\partial u| \le V|u|$, where u is a vector-valued function from a domain in Cn to CN, 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>1. In both cases, the L2 integrability condition on the potential is optimal.
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| Acknowledgements
N/A
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| Author information
Yifei Pan
Department of Mathematical Sciences
Purdue University Fort Wayne
Fort Wayne, IN 46805-1499, USA
pan@pfw.edu
Yuan Zhang
Department of Mathematical Sciences
Purdue University Fort Wayne
Fort Wayne, IN 46805-1499, USA
zhangyu@pfw.edu
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