Compact embedding in the space of piecewise H1 functions
Numerical Analysis
2013-03-01 v1
Abstract
We prove a compact embedding theorem in a class of spaces of piecewise H1 functions subordinated to a class of shape regular, but not necessarily quasi-uniform triangulations of a polygonal domain. This result generalizes the Rellich--Kondrachov theorem. It is used to prove generalizations to piecewise functions of nonstandard Poincar\'e--Friedrichs inequalities. It can be used to prove Korn inequalities for piecewise functions associated with elastic shells.
Cite
@article{arxiv.1302.7079,
title = {Compact embedding in the space of piecewise H1 functions},
author = {Sheng Zhang},
journal= {arXiv preprint arXiv:1302.7079},
year = {2013}
}