Bulletin of the
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Bull. Korean Math. Soc. 2015; 52(5): 1753-1757

Printed September 30, 2015

https://doi.org/10.4134/BKMS.2015.52.5.1753

Copyright © The Korean Mathematical Society.

A remark on unique continuation for the Cauchy-Riemann operator

Ihyeok Seo

Sungkyunkwan University

Abstract

In this note we obtain a unique continuation result for the differential inequality $|\overline{\partial}u|\leq|Vu|$, where $\overline{\partial}=(i\partial_y+\partial_x)/2$ denotes the Cauchy-Riemann operator and $V(x,y)$ is a function in $L^2(\mathbb{R}^2)$.

Keywords: unique continuation, Cauchy-Riemann operator

MSC numbers: Primary 35B60, 35F05

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