Partial expansion of a Lipschitz domain and some applications

Abstract

We show that a Lipschitz domain can be expanded solely near a part of its boundary, assuming that the part is enclosed by a piecewise C¹ curve. The expanded domain as well as the extended part are both Lipschitz. We apply this result to prove a regular decomposition of standard vector Sobolev spaces with vanishing traces only on part of the boundary. Another application in the construction of low-regularity projectors into finite element spaces with partial boundary conditions is also indicated.

Keywords

Lipschitz domain / regular decomposition / mixed boundary condition / transversal vector field / extension operator / Schwarz preconditioner / bounded cochain projector / divergence / curl / Schöberl projector

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