Generalized and strong solutions for an elliptic system 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 non connected. We establish an appropriate Inf-Sup condition and then we prove the existence and uniqueness of the generalized solutions in Lp-Theory. We also investigate the case of strong solutions.