A compactness result for vector fields with divergence and curl in L^q(ω) involving mixed boundary conditions

Abstract

It is shown that the space of all vector fields with divergence and curl in L^q(ω)q≤2 such that the normal-component vanishes on one part of ∂̸ω and the tangential-component vanishes on the other, is compactly imbedded in L²(ω)

Keywords:

• Weakly differentiable functions
• compact imbeddings
• mixed boundary bconditions