scholarly journals Note on Friedrichs' inequality in N-star-shaped domains

2016 ◽  
Vol 435 (2) ◽  
pp. 1514-1524 ◽  
Author(s):  
Reinhard Farwig ◽  
Veronika Rosteck
Keyword(s):  
Friedrichs Inequality

On the Discrete Friedrichs Inequality for Nonconforming Finite Elements

1999 ◽  
Vol 20 (5-6) ◽  
pp. 437-447 ◽  
Author(s):  
Vít Dolejší ◽  
Miloslav Feistauer ◽  
Jiří Felcman
Keyword(s):  
Finite Elements ◽  
Nonconforming Finite Elements ◽  
Friedrichs Inequality

A Friedrichs inequality and an application

1984 ◽  
Vol 97 ◽  
pp. 185-191 ◽  
Author(s):  
Roger T. Lewis
Keyword(s):  
Differential Operators ◽  
Arbitrary Order ◽  
Type Inequality ◽  
Essential Spectra ◽  
Hardy Type Inequality ◽  
Hardy Type ◽  
Partial Differential Operators ◽  
Even Order ◽  
Friedrichs Inequality ◽  
Derivatives Of

SynopsisAn inequality whose origins date to the work of G. H. Hardy is presented. This Hardy-type inequality applies to derivatives of arbitrary order of functions whose domain is a subset of ℝn. The Friedrichs inequality is a corollary. The result is then used to establish lower bounds on the essential spectra of even-order elliptic partial differential operators on unbounded domains.

Poincaré and Friedrichs inequalities in abstract Sobolev spaces II

1994 ◽  
Vol 115 (1) ◽  
pp. 159-173 ◽  
Author(s):  
D. E. Edmunds ◽  
B. Opic ◽  
J. Rákosník
Keyword(s):  
Banach Space ◽  
Sobolev Space ◽  
Weight Function ◽  
Sobolev Spaces ◽  
Positive Constant ◽  
Banach Function Spaces ◽  
Distributional Derivative ◽  
Friedrichs Inequality ◽  
Image Position ◽  
Anisotropic Spaces

This paper is a continuation of [4]; its aim is to extend the results of that paper to include abstract Sobolev spaces of higher order and even anisotropic spaces. Let Ω be a domain in ℝN, let X = X(Ω) and Y = Y(Ω) be Banach function spaces in the sense of Luxemburg (see [4] for details), and let W(X, Y) be the abstract Sobolev space consisting of all f ∈ X such that for each i ∈ {l, …, N} the distributional derivative belongs to Y; equipped with the normW(X, Y) is a Banach space. Given any weight function w on Ω, the triple [w, X, Y] is said to support the Poincaré inequality on Ω. if there is a positive constant K such that for all u ∈ W(X, Y)the pair [X, Y] is said to support the Friedrichs inequality if there is a positive constant K such that for all u ∈ W0(X, Y) (the closure of in W(X, Y))

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