  We show that the elasticity Hilbert complex with mixed boundary conditions on
bounded strong Lipschitz domains is closed and compact. The crucial results are
compact embeddings which follow by abstract arguments using functional analysis
together with particular regular decompositions. Higher Sobolev order results
are proved as well. This paper extends recent results on the de Rham Hilbert
complex with mixed boundary conditions from [11] and recent results on the
elasticity Hilbert complex with empty or full boundary conditions from [15].
