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arXiv · 2104.09659

The $\bar{\partial}$-Neumann problem and boundary integral equations

Bingyuan Liu
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Abstract

In this note, we find an equivalent boundary integral equation to the classical $\bar{\partial}$-Neumann problem. The new equation contains an equivalent regularity to the global regularity of the $\bar{\partial}$-Neumann problem. We also use the integral equations to observe a new-found rigidity property of the $\bar{\partial}$-Neumann problem on the unit ball in $\mathbb{C}^2$.

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Bingyuan Liu. 2021-04-19. The $\bar{\partial}$-Neumann problem and boundary integral equations. https://arxiv.org/abs/2104.09659

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