In this paper we give the definition of 1/2-harmonic maps u : D → N , where D is an open set of IR and N is a k dimensional submanifold N of IRm as critical points of the functional ∫ Ω |∆ 1/4u|2dx . We write the Euler-Lagrange equation satisfied in a weak sense by the 1/2-harmonic maps, which is a nonlocal partial differential equation involving the 1/2-Laplacian operator . We prove the local ...

We study the regularity properties of generalized solutions of the EulerLagrange equation of a functional involving capacity and perimeter, related to a conjecture of Pólya and Szegö.

A surface of codimension higher than one embedded in an ambient space possesses a connection associated with the rotational freedom of its normal vector fields. We examine the Yang-Mills functional associated with this connection. The theory it defines differs from Yang-Mills theory in that it is a theory of surfaces. We focus, in particular, on the Euler-Lagrange equations describing this surf...

Calculus of variations on time scales (we refer the reader to Section 2 for a brief introduction to time scales) has been introduced in 2004 in the papers by Bohner [2] and Hilscher and Zeidan [4], and seems to have many opportunities for application in economics [1]. In both works of Bohner and Hilscher&Zeidan, the Euler-Lagrange equation for the fundamental problem of the calculus of variatio...

The smoothing properties of variational methods for the design of fair surfaces are considered using a PDE (partial differential equation) model. The PDE is the Euler-Lagrange equation that is obtained from the variational formulation of the surface design problem. The smoothing properties of the design scheme are considered by looking at the scheme's efficiency in reducing the amplitude of the...

In this paper we show how to compute algorithmically the full set of algebraically independent constraints for singular mechanical and field-theoretical models with polynomial Lagrangians. If a model under consideration is not singular as a whole but has domains of dynamical (field) variables where its Lagrangian becomes singular, then our approach allows to detect such domains and compute the ...

We consider a D-dimensional cosmological model describing an evolution of (n+1) Einstein factor spaces (n ≥ 2) in the theory with several dilatonic scalar fields and generalized electro-magnetic forms, admitting an interpretation in terms of intersecting p-branes. The equations of motion of the model are reduced to the Euler-Lagrange equations for the so called pseudo-Euclidean Toda-like system...

The Cauchy problem for harmonic maps from Minkowski space with its standard flat metric to a certain non-constant curvature Lorentzian 2-metric is studied. The target manifold is distinguished by the fact that the Euler–Lagrange equation for the energy functional is Darboux integrable. The time evolution of the Cauchy data is reduced to an ordinary differential equation of Lie type associated t...

I. PROBLEM FORMULATION The Furuta pendulum consists of an arm rotating in the horizontal plane and a pendulum attached to the end of the arm moving freely in the vertical plane, see Fig. 1. The equations of motion of the Furuta pendulum, derived from the standard Euler-Lagrange dynamics, are1 (α + β sin θ)φ̈ + γ cos θθ̈ + 2βθ̇φ̇ sin θ cos θ − γθ̇ sin θ = τφ, γ cos θφ̈ + βθ̈ − βφ̇ sin θ cos θ − δ sin θ ...

We present an explicit polynomial solution method for surface generation. In this case the surface in question is characterized by some boundary configuration whereby the resulting surface conforms to a fourth order linear elliptic Partial Differential Equation, the Euler-Lagrange equation of a quadratic functional defined by a norm. In particular, the paper deals with surfaces generated as exp...