Korn's inequalities for piecewise H1 vector fields

Korn’s Inequalities for Piecewise H Vector Fields

Korn’s inequalities for piecewise H1 vector fields are established. They can be applied to classical nonconforming finite element methods, mortar methods and discontinuous Galerkin methods.

Eigenvalue Problems Associated with Korn's Inequalities

. Korn and Korn - like inequalities for perfect cylindrical shells by Davit Harutyunyan

It is well known that Korn's inequality plays a central role in the theory of linear elasticity. In their recent work Grabovsky and Truskinovsky (2007) proved a connection between the Korn inequalities and buckling problems coming from nonlinear elasticity. It has been shown that when the general buckling theory by Grabovsky and Truskinovsky is applicable, then Korn's inequality gives a lower b...

On the Closing Lemma for Planar Piecewise Smooth Vector Fields

A large number of papers deal with “Closing Lemmas” for Cr-vector fields (and Cr-diffeomorphisms). Here, we introduce this subject and formalize the terminology about nontrivially recurrent points and nonwandering points for the context of planar piecewise smooth vector fields. A global bifurcation analysis of a special family of piecewise smooth vector fields presenting a nonwandering set with...

Stable Piecewise Polynomial Vector Fields

Let N = {y > 0} and S = {y < 0} be the semi-planes of R2 having as common boundary the line D = {y = 0}. Let X and Y be polynomial vector fields defined in N and S, respectively, leading to a discontinuous piecewise polynomial vector field Z = (X, Y ). This work pursues the stability and the transition analysis of solutions of Z between N and S, started by Filippov (1988) and Kozlova (1984) and...