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Displaying 141 –
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332
Let be an open half-space or slab in ℝn+1 endowed with a perturbation of the Gaussian measure of the form f (p) := exp(ω(p) − c|p|2), where c > 0 and ω is a smooth concave function depending only on the signed distance from the linear hyperplane parallel to ∂ Ω. In this work we follow a variational approach to show that half-spaces perpendicular to ∂ Ω uniquely minimize the weighted perimeter in Ω among sets enclosing the same weighted volume. The main ingredient of the proof is the characterization...
In the presented paper we apply the theory of Lepage forms on jet prolongations of fibred manifold with one-dimensional base to the relativistic mechanics. Using this geometrical theory, we obtain and discuss some well-known conservation laws in their general form and apply them to a concrete physical example.
Si studia il comportamento limite di successioni di problemi variazionali nonlineari con condizioni al contorno di Dirichlet su aperti variabili. I principali strumenti usati in questa ricerca sono le nozioni di -convergenza e di -capacità nonlineare.
This paper gives a rigorous derivation
of a functional proposed by Aftalion and Rivière [Phys. Rev. A64 (2001) 043611]
to characterize the energy of vortex filaments
in a rotationally forced Bose-Einstein condensate. This
functional is derived as a Γ-limit
of scaled versions of the Gross-Pitaevsky
functional for the wave function of such a condensate. In most situations,
the vortex filament energy functional is either unbounded below
or has only trivial minimizers, but
we establish the existence...
We prove that any Kantorovich potential for the cost function c = d2/2 on a Riemannian manifold (M, g) is locally semiconvex in the “region of interest”, without any compactness assumption on M, nor any assumption on its curvature. Such a region of interest is of full μ-measure as soon as the starting measure μ does not charge n – 1-dimensional rectifiable sets.
We prove that any Kantorovich potential for the cost function
c = d2/2 on a Riemannian manifold (M, g) is locally semiconvex
in the “region of interest”, without any compactness assumption
on M, nor any assumption on its curvature. Such a region of
interest is of full μ-measure as soon as the starting measure
μ does not charge n – 1-dimensional rectifiable sets.
New -lower semicontinuity and relaxation results for integral functionals defined in BV() are proved, under a very weak dependence of the integrand with respect to the spatial variable . More precisely, only the lower semicontinuity in the sense of the -capacity is assumed in order to obtain the lower semicontinuity of the functional. This condition is satisfied, for instance, by the lower approximate limit of the integrand, if it is BV with respect to . Under this further BV dependence, a...
New L1-lower semicontinuity and relaxation results for integral functionals defined in BV(Ω) are proved,
under a very weak dependence of the integrand with respect to the spatial variable x. More
precisely, only the lower semicontinuity in the sense of the 1-capacity is assumed in
order to obtain the lower semicontinuity of the functional.
This condition is satisfied, for instance, by the lower approximate limit of the integrand, if
it is BV with respect to x. Under this further BV dependence,
a...
We discuss a numerical formulation for the cell problem related to a homogenization approach for the study of wetting on micro rough surfaces. Regularity properties of the solution are described in details and it is shown that the problem is a convex one. Stability of the solution with respect to small changes of the cell bottom surface allows for an estimate of the numerical error, at least in two dimensions. Several benchmark experiments are presented and the reliability of the numerical solution...
The left-invariant sub-Riemannian problem on the group of motions of a plane is considered. Sub-Riemannian geodesics are parameterized by Jacobi's functions. Discrete symmetries of the problem generated by reflections of pendulum are described. The corresponding Maxwell points are characterized, on this basis an upper bound on the cut time is obtained.
Currently displaying 141 –
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332