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

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