We prove stochastic homogenization for integral functionals defined on Sobolev spaces, where the stationary, ergodic integrand satisfies a degenerate growth condition of form c|ξA(ω,x)| p ≤f(ω,x,ξ)≤|ξA(ω,x)| +Λ(ω,x) some p∈(1,+∞) and with stationary diagonal matrix A such that its norm inverse satisfy minimal integrability assumptions Λ is nonnegative, function finite first moment. also conside...

A variational principle is introduced which minimizes an action formulated for configurations of vacuum Dirac seas. The action is analyzed in position and momentum space. We relate the corresponding Euler-Lagrange equations to the notion of state stability. Examples of numerical minimizers are constructed and discussed.

We describe some numerical techniques for the Total Variation image restoration method, namely a primal-dual linearization for the Euler-Lagrange equations and some preconditioning issues. We also highlight extension of this technique to color images, blind de-convolution and the staircasing eeect.

This paper gives a common theoretical treatment for gradient and Newton type methods for general classes of problems. First, for Euler-Lagrange equations Newton’s method is characterized as an (asymptotically) optimal variable steepest descent method. Second, Sobolev gradient type minimization is developed for general problems using a continuous Newton method which takes into account a ‘boundar...

The classical Euler-Poisson equations describing the motion of a heavy rigid body about a fixed point are generalized to arbitrary Lie algebras as Hamiltonian systems on coad-joint orbits of a tangent bundle Lie group. the N-dimensional Lagrange and symmetric heavy top are thereby shown to be completely integrable.

We derive Euler-Lagrange type equations for fractional action-like integrals of the calculus of variations which depend on the Riemann-Liouville derivatives of order (α, β), α > 0, β > 0, recently introduced by J. Cresson and S. Darses. Some interesting consequences are obtained and discussed. Mathematics Subject Classification 2000: 49K05, 49S05, 70H33, 26A33.

It is possible to introduce external time dependent back ground fields in the formulation of a system as fields whose dynamics can not be deduced from Euler Lagrange equations of motion. This method leads to singular Lagrangians for real systems. We discuss quantization of constraint systems in these cases and introduce generalized Gupta-Bleuler quantization. In two examples we show explicitly ...

We verify -after appropriate modificationsan old conjecture of Brezis-Ekeland [3] concerning the feasibility of a global and variational approach to the problems of existence and uniqueness of solutions of non-linear transport equations, which do not normally fit in an Euler-Lagrange framework. Our method is based on a concept of “anti-self duality” that seems to be inherent in many problems, i...

Abstract: It is assumed that a beam made of material has a physical nonlinear behavior. This beam is analyzed under the moving concentrated and distributed continuous loads. The vibration equations of motion are derived from the Hamilton's Principle and Euler–Lagrange Equation. In this study, the amplitude of vibration, circular frequency, bending moment, stress and deflection of the beam has b...