Jochmann, Frank
A compactness result for vector fields with divergence and curl in $L^q(\Omega)$ involving mixed boundary conditions
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)

MSC:

35F05 General theory of linear first-order PDE

46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems

Abstract:It is shown that the space of all vector fields with divergence and curl in $L^q(\Omega)$, $q\le 2$ such that the normal-component vanishes one part of $\partial\Omega$ and the tangential- component vanishes on the other, is compactly imbedded in $L^2(\Omega)$.
Keywords: Weakly differentiable functions, compact imbeddings, mixed boundary conditions