 
Summary: DIVERGENCE L2
COERCIVITY INEQUALITIES.
GILES AUCHMUTY
Abstract. This paper describes sharp L2
coercivity inequalities for the divergence
operator on bounded Lipschitz regions in Rn
. The inequalities are given in a manner
which scales under dilations of the region. The optimal constants in the inequality are
identified as the least eigenvalue of a biharmonic problem or else of a nonstandard
problem for the Dirichlet Laplacian. When n = 2, a coercivity result for the curl
operator is also obtained.
1. Introduction
An important class of estimates for the analysis of elliptic boundary value prob
lems are Friedrichs' type inequalities such as
(1.1)
 2
dn
x +
