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 (Formula presented.) -theory. We also investigate the case of strong solutions.