On $\varepsilon$-Friedrichs inequalities and its application

On Friedrichs – Poincaré - type inequalities ✩

Friedrichsand Poincaré-type inequalities are important and widely used in the area of partial differential equations and numerical analysis. Most of their proofs appearing in references are the argument of reduction to absurdity. In this paper, we give direct proofs of Friedrichs-type inequalities in H 1(Ω) and Poincaré-type inequalities in some subspaces of W1,p(Ω). The dependencies of the ine...

On the inequalities of Babuška-Aziz, Friedrichs and Horgan-Payne

The equivalence between the inequalities of Babuška–Aziz and Friedrichs for sufficiently smooth bounded domains in the plane has been shown by Horgan and Payne 30 years ago. We prove that this equivalence, and the equality between the associated constants, is true without any regularity condition on the domain. For the Horgan–Payne inequality, which is an upper bound of the Friedrichs constant ...

construction and validation of translation metacognitive strategy questionnaire and its application to translation quality

like any other learning activity, translation is a problem solving activity which involves executing parallel cognitive processes. the ability to think about these higher processes, plan, organize, monitor and evaluate the most influential executive cognitive processes is what flavell (1975) called “metacognition” which encompasses raising awareness of mental processes as well as using effectiv...

Dirichlet integrals and Gaffney-Friedrichs inequalities in convex domains

We study geometrical conditions guaranteeing the validity of the classical GaffneyFriedrichs estimate ‖u‖H1,2(Ω) ≤ C ( ‖du‖L2(Ω) + ‖δu‖L2(Ω) + ‖u‖L2(Ω) ) (0.1) granted that the differential form u has a vanishing tangential or normal component on ∂Ω. Our main result is that (0.1) holds provided Ω satisfies a suitable convexity assumption. In the Euclidean setting, a uniform exterior ball condit...

Poincar E and Friedrichs Inequalities for Mortar Finite Element Methods