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Dependence of Friedrichs' constant on boundary integrals

Published online by Cambridge University Press:  12 July 2007

Giles Auchmuty ,
Behrouz Emamizadeh  and
Mohsen Zivari
Giles Auchmuty
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA (auchmuty@uh.edu)
Behrouz Emamizadeh
Affiliation:
Department of Mathematics, The Petroleum Institute, PO Box 2533, Abu Dhabi, United Arab Emirates (bemamizadeh@pi.ac.ae)
Mohsen Zivari
Affiliation:
Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran (m_zivari@iust.ac.ir)
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Abstract

This note extends the results in ‘Optimal coercivity inequalities in W1,p(Ω)’ (G. Auchmuty, Proc. R. Soc. Edinb. A 135, 915–933.) 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 → ∞.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 5 , October 2005 , pp. 935 - 939
Copyright
Copyright © Royal Society of Edinburgh 2005

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