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Displaying 41 –
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The theory of variational bicomplexes is a natural geometrical setting for the calculus of variations on a fibred manifold. It is a well–established theory although not spread out very much among theoretical and mathematical physicists. Here, we present a new approach to infinite order variational bicomplexes based upon the finite order approach due to Krupka. In this approach the information related to the order of jets is lost, but we have a considerable simplification both in the exposition...
For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first jet bundle of a principal bundle. It is shown that covariant and dynamic reduction lead to equivalent equations of motion. This is achieved by constructing a new Lagrangian defined on an infinite dimensional space which turns out to be gauge group invariant.
A new model for propagation of long waves including the coastal area is introduced. This model considers only the motion of the surface of the sea under the condition of preservation of mass and the sea floor is inserted into the model as an obstacle to the motion. Thus we obtain a constrained hyperbolic free-boundary problem which is then solved numerically by a minimizing method called the discrete Morse semi-flow. The results of the computation in 1D show the adequacy of the proposed model.
In this paper we consider a nonlinear periodic system driven by the vector ordinary -Laplacian and having a nonsmooth locally Lipschitz potential, which is positively homogeneous. Using a variational approach which exploits the homogeneity of the potential, we establish the existence of a nonconstant solution.
The first motivation for this note is to obtain a general version
of the following result: let E be a Banach space and f : E → R be a differentiable
function, bounded below and satisfying the Palais-Smale condition; then, f is coercive,
i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and
extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references
therein.
A general result of this type was given in [3, Theorem 5.1] for a lower...
We describe a new link between Perelman’s monotonicity formula for the reduced volume and ideas from optimal transport theory.
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