Lp‐theory for elliptic systems without divergence constraint and with Navier‐type boundary condition

Abstract

In this paper, we study a linear elliptic system involving Navier‐type boundary conditions or tangential components in a three‐dimensional bounded domain, possibly multiply connected and with boundary possibly nonconnected. We establish an appropriate Inf‐Sup condition and then we prove the existence and uniqueness of the generalized solutions in ‐theory. We also investigate the case of strong solutions.