Summary: DEPENDENCE OF FRIEDRICHS' CONSTANT ON BOUNDARY
INTEGRALS.
GILES AUCHMUTY, BEHROUZ EMAMIZADEH AND MOHSEN ZIVARI
Abstract. This note extends the results in [2], by describing the dependence of the
optimal constant in the p-version of Friedrichs' inequality on the boundary integral
term. In particular, it is shown that this constant is continuous, increasing, concave
and increases to the optimal constant for the Dirichlet problem as s .
1. Introduction
Recently in [2], the optimal constants in the inequality
(1.1)

N
j=1
|Dj u|p
dx +

b|u|p
d CF

|u|p

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

Collections: Mathematics