Dependence of Friedrichs' constant on boundary integrals

Giles Auchmuty; Behrouz Emamizadeh; Mohsen Zivari

doi:10.1017/S0308210500004194

Dependence of Friedrichs' constant on boundary integrals

Giles Auchmuty, Behrouz Emamizadeh, Mohsen Zivari

Research output: Journal Publication › Article › peer-review

2 Citations (Scopus)

Abstract

This note extends the results in 'Optimal coercivity inequalities in W ^1,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 → ∞.

Original language	English
Pages (from-to)	935-939
Number of pages	5
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	135
Issue number	5
DOIs	https://doi.org/10.1017/S0308210500004194
Publication status	Published - 2005
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1017/S0308210500004194

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AU - Zivari, Mohsen

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N2 - This note extends the results in 'Optimal coercivity inequalities in W 1,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 → ∞.

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Dependence of Friedrichs' constant on boundary integrals

Abstract

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