This paper builds on the initial work of Marsden and Scheurle on nonabelian Routh reduction. The main objective of the present paper is to carry out the reduction of variational principles in further detail. In particular, we obtain reduced variational principles which are the symplectic analogue of the well known reduced variational principles for the Euler{Poincar e equations and the Lagrange...

We derive a new variational principle in optics. We first formulate the principle for paraxial waves and then generalize it to arbitrary waves. The new principle, unlike the Fermat principle, concerns both the phase and the intensity of the wave. In particular, the principle provides a method for finding the ray mapping between two surfaces in space from information on the wave's intensity ther...

This paper introduces new types of Euler-Lagrange PDEs required by optimal control problems with performance criteria involving curvilinear or multiple integrals subject to evolutions of multidimensional-flow type. Particularly, the anti-trace multi-time Euler-Lagrange PDEs are strongly connected to the multi-time maximum principle. Section 1 comments the limitations of classical multi-variable...

This paper is concerned with the existence of two non-trivial weak solutions for a p(x)-Kirchho type problem by using the mountain pass theorem of Ambrosetti and Rabinowitz and Ekeland's variational principle and the theory of the variable exponent Sobolev spaces.

Constructive Mathematics Simon Fraser University Burnaby BC Canada Lake Gargnano, Sept. 13{17, 1999 URL: www. e m.sfu. a/personal/jborwein Papers: www. e m.sfu. a/preprints/1 ABSTRACT. I will des ribe the basi ideas from Bana h spa e theory that allow one to fruitfully apply notions from smooth analysis in spa es whi h do not admit smooth renorms (or \bumps") and so to perform Partially Smooth ...

We consider the following nonlinear singular elliptic equation −div (|x| −2a ∇u) = K(x)|x| −bp |u| p−2 u + λg(x) in R N , where g belongs to an appropriate weighted Sobolev space, and p denotes the Caffarelli–Kohn– Nirenberg critical exponent associated to a, b, and N. Under some natural assumptions on the positive potential K(x) we establish the existence of some λ 0 > 0 such that the above pr...

This paper is concerned with the existence of nontrivial solutions for a class of degenerate quasilinear elliptic systems involving critical Hardy-Sobolev type exponents. The lack of compactness is overcame by using the Brezis-Nirenberg approach, and the multiplicity result is obtained by combining a version of the Ekeland’s variational principle due to Mizoguchi with the Ambrosetti-Rabinowitz ...

A general variational principle of classical fields with a Lagrangian containing field quantity and its derivatives of up to the N-order is presented. Noether’s theorem is derived. The generalized Hamilton-Jacobi’s equation for the Hamilton’s principal functional is obtained. These results are surprisingly in great harmony with each other. They will be applied to general relativity in the subse...

I find conditions under which the ”Weak Energy Principle” of Katz, Inagaki and Yahalom (1993) gives necessary and sufficient conditions. My conclusion is that, necessary and sufficient conditions of stability are obtained when we have only two mode coupling in the gyroscopic terms of the perturbed Lagrangian. To illustrate the power of this new energy principle, I have calculated the stability ...