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 non-standard
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 +

Source: Auchmuty, Giles - Department of Mathematics, University of Houston

Collections: Mathematics