Problems in incompressible linear elasticity involving tangential and normal components of the displacement field

Abstract

We consider the linear system -∆ u + grad p = f plus the divergence-free condition div u = O, in a bounded and conected but non simply connected open set Ω of R³, with a boundary ᴦ of C∞ class. Using orthogonal decompositions of the Hilbert space of square integrable vector fields on Ω, we show well posedness for two boundary value problems involving normal or tangential components of the displacement field on ᴦ.