We introduce two three-field mixed formulations for the Poisson equation and propose finite element methods for their approximation. Both mixed formulations are obtained by introducing a weak equation for the gradient of the solution by means of a Lagrange multiplier space. Two efficient numerical schemes are proposed based on using a pair of bases for the gradient of the solution and the Lagra...

The problem of minimal distortion bending of smooth compact embedded connected Riemannian n-manifolds M and N without boundary is made precise by defining a deformation energy functional Φ on the set of diffeomorphisms Diff(M,N). We derive the Euler-Lagrange equation for Φ and determine smooth minimizers of Φ in case M and N are simple closed curves. MSC 2000 Classification: 58E99

Under the bounded slope condition on the boundary values of a minimization problem for a functional of the gradient of u, we show that a continuous minimizer w is, in fact, Lipschitzian. An application of this result to prove the validity of the Euler Lagrange equation for w is presented.

I have used a novel approach based upon Hamiltonian mechanics to derive new equations for nearly geostrophic motion in a shallow homogeneous fluid. The equations have the same order accuracy as (say) the quasigeostrophic equations, but they allow order-one variations in the depth and Coriolis parameter. My equations exactly conserve proper analogues of the energy and potential vorticity, and th...

In a recent paper [7] we interpreted configurational forces as necessary and sufficient dissipative mechanisms such that the corresponding Euler-Lagrange equations are satisfied. We now extend this argument for a dynamic elastic medium, and show that the energy flux obtained from the dynamic J integral ensures that the equations of motion hold throughout the body.

A general model of solids with vectorial microstructures is introduced. The field equationsare the obtained as Euler-Lagrange equations of a suitable energetic functional. The Cosserat model is encompassed in this model and it can be used to study the behaviour of granular media. A first approach to this problem deals with a two dimensional model, since in such a case the field equations have a...

We introduce a generalized additivity of a mapping between Banach spaces and establish the Ulam type stability problem for a generalized additive mapping. The obtained results are somewhat different from the Ulam type stability result of Euler-Lagrange type mappings obtained by H. -M. Kim, K. -W. Jun and J. M. Rassias.

In this paper we investigate the following question: under what conditions can a second-order homogeneous ordinary differential equation (spray) be the geodesic equation of a Finsler space. We show that the EulerLagrange partial differential system on the energy function can be reduced to a first order system on this same function. In this way we are able to give effective necessary and suffici...

In this manuscript we are interested in stored energy functionals W defined on the set of d × d matrices, which not only fail to be convex but satisfy limdet ξ→0+ W (ξ) = ∞. We initiate a study which we hope would lead to a theory for the existence and uniqueness of minimizers of functionals of the form E(u) = ∫ Ω (W (∇u) − F · u)dx, as well as their Euler–Lagrange equations. The techniques dev...

The equations of motion of multibody systems with holonomic constraints are of index 3 and therefore not directly solvable by standard ODE or DAE methods. Until now, a number of regularization methods have been proposed to treat these systems [1, 2, 3, 4], but as they are based on different points of view they have never been compared with respect to their physical properties, invariance under ...