Boundary integral operators over Lipschitz surfaces for a Stokes equation in \(\mathbb R^{n}\) (Q944293)

Let \(\Omega \) be a bounded Lipschitz domain in \(\mathbb R^{n}\), where \( n\geq 3\), and let \(\Gamma \) be a proper open subset of \(\partial \Omega \). The author shows, in particular, that problems of the following form have unique solutions: \(\Delta \mathbf{u}=\nabla p\) and \(\operatorname{div}\mathbf{u}=0\) in \(\mathbb R^{n}\backslash \Gamma \), and \(\mathbf{u}_{| \Gamma }=g\in \mathbf{H}^{1/2}(\Gamma )\) on \(\Gamma \).