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

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 ${\mathbb{C}}^2$.

Mistakes corrected

References in corpus (1)

• The Diederich--Fornæss index and the regularities on the $\bar{\partial }$-Neumann problem