Short time scale variations have been reported for a few Miras, including sudden 0.2 magnitude or more brightening in the visual lasting from a few hours to a few days. Are these flashes real? Are they hot? What are they? Almost all the natural time scales for variation in the atmosphere and wind of a Mira variable are months to years long. What could cause such short-term variations? One intri...

We prove variational and jump inequalities for a large class of linear operators arising in harmonic analysis.

In §1 the authors present the basic properties of the scalar product along a curve on a Finsler manifold. In §2 they investigate the variational formulae for the p-energy functional (p ∈ R − {0}). This concept generalises the notions of length (p = 1) and energy (p = 2) of a curve. §3 analyses the extrema of p-energy when the Finsler space has constant curvature. (F3) the fundamental tensor g i...

The calculus of variations for lagrangians which are not functions on the tangent bundle, but sections certain affine bundles is developed. We follow a general approach to variational principles which admits boundary terms of variations. MSC 2000: 70G45, 70H03, 70H05

This is a self-contained paper which introduces a fundamental problem in the calculus of variations, the problem of finding extreme values of functionals. The reader should have a solid background in onevariable calculus.

We introduce a class of variational principles on measure spaces which are causal in the sense that they generate a relation on pairs of points, giving rise to a distinction between spacelike and timelike separation. General existence results are proved. It is shown in examples that minimizers need not be unique. Counter examples to compactness are discussed. The existence results are applied t...

We look for necessary and sufficient conditions for the existence of solutions of the minimization problem (P) inf Ω f (P Du(x)) dx : u ∈ u ζ 0 + W m,∞ 0 (Ω; R N) where P D is a particular type of differential operator of order m, (which we identify as of divergence type) and the boundary data u ζ 0 satisfes P Du ζ 0 (x) = ζ0 for ζ0 ∈ R given.

Keywords: Second order differential systems Saddle point theorem Generalized Ahmad–Lazer–Paul type condition a b s t r a c t Existence of periodic solutions to second order differential systems with gyroscopic forces is considered via variational methods, where a generalized Ahmad–Lazer–Paul type condition is used. We do not impose the condition that the gyroscopic forces are small.

Fractional (non-integer) derivatives and integrals play an important role in theory and applications. The fractional calculus of variations is a rather recent subject with the first results from 1996. This paper presents necessary and sufficient optimality conditions for fractional problems of the calculus of variations with a Lagrangian density depending on the free end-points. The fractional ...

We consider local minimizers u : R 2 ⊃ Ω → R M of the variational integral Ω H(∇u) dx with density H growing at least quadratically and allowing a very large scale of anisotropy. We discuss higher integrability properties of ∇u as well as the differentiability of u in the classical sense. Moreover, a Liouville-type theorem is established.