We discuss Lagrange multiplier rules from a variational perspective. This allows us to highlight many of the issues involved and also to illustrate how broadly an abstract version can be applied.

We examine the ADM reformulation of the 5-D KK model: the dimensional reduction is provided to commute with the ADM splitting and we show how the time component of the gauge vector is given by combination of the Lagrangian multipliers for the 5D gravitational field. We consider 5D particles motion and after dimensional reduction the definition of charge is recovered within electrodynamic coupli...

Spectral properties of periodic nonreciprocal (gyrotropic) electric circuits incorporating gyrators are studied. Based on the Lagrange formalism we analyze the origin of the special features of periodic nonreciprocal media and establish some universal spectral properties common for a variety of gyrotropic periodic systems. We found that the combination of periodicity and nonreciprocity can prod...

The effect of fluctuations about the π-flux mean field state for the undoped hightemperature superconductors is investigated. It is shown that fluctuations of the mean fields lead to a self-energy correction that doubles the band width of the fermion dispersion in the lowest order. The dynamical mass generation is associated with the self-energy effect due to the interaction mediated by the Lag...

Theorem (PontryaginMaximum Principle). Suppose a final time T and controlstate pair (û, x̂) on [τ, T ] give the minimum in the problem above; assume that û is piecewise continuous. Then there exist a vector of Lagrange multipliers (λ0, λ) ∈ R × R with λ0 ≥ 0 and a piecewise smooth function p: [τ, T ] → R n such that the function ĥ(t) def =H(t, x̂(t), p(t), û(t)) is piecewise smooth, and one has ̇̂ ...

The initial boundary value problem for a class of nonlinear higher-order wave equation with damping and source term utt Au a|ut|ut b|u|q−1u in a bounded domain is studied, where A −Δ , m ≥ 1 is a nature number, and a, b > 0 and p, q > 1 are real numbers. The existence of global solutions for this problem is proved by constructing the stable sets and shows the asymptotic stability of the global ...

We consider the classical Besov and Triebel-Lizorkin spaces defined via differences and prove a homogeneity property for functions with bounded support in the frame of these spaces. As the proof is based on compact embeddings between the studied function spaces we present also some results on the entropy numbers of these embeddings. Moreover, we derive some applications in terms of pointwise mu...

We investigate three classes of constraints in a thermoelastic body: (i) a deformationtemperature constraint, (ii) a deformation-entropy constraint, and (iii) a deformationenergy constraint. These constraints are obtained as limits of unconstrained thermoelastic materials and we show that constraints (ii) and (iii) are equivalent. By using a limiting procedure, we show that for the constraint (...