4,520 research outputs found
Hypercontractivity and asymptotic behaviour in nonautonomous Kolmogorov equations
We consider a class of nonautonomous second order parabolic equations with
unbounded coefficients defined in , where is a right-halfline.
We prove logarithmic Sobolev and Poincar\'e inequalities with respect to an
associated evolution system of measures , and we deduce
hypercontractivity and asymptotic behaviour results for the evolution operator
Asymptotic behavior in time periodic parabolic problems with unbounded coefficients
We study asymptotic behavior in a class of non-autonomous second order
parabolic equations with time periodic unbounded coefficients in . Our results generalize and improve asymptotic behavior
results for Markov semigroups having an invariant measure. We also study
spectral properties of the realization of the parabolic operator in suitable spaces
On coupled systems of Kolmogorov equations with applications to stochastic differential games
We prove that a family of linear bounded evolution operators can be associated, in the space of vector-valued
bounded and continuous functions, to a class of systems of elliptic operators
with unbounded coefficients defined in I\times \Rd (where
is a right-halfline or ) all having the same principal part. We
establish some continuity and representation properties of and a sufficient condition for the evolution operator to be
compact in C_b(\Rd;\R^m). We prove also a uniform weighted gradient estimate
and some of its more relevant consequence
Kernel estimates for nonautonomous Kolmogorov equations
Using time dependent Lyapunov functions, we prove pointwise upper bounds for
the heat kernels of some nonautonomous Kolmogorov operators with possibly
unbounded drift and diffusion coefficients
A Five Dimensional Perspective on Many Particles in the Snyder basis of Double Special Relativity
After a brief summary of Double Special Relativity (DSR), we concentrate on a
five dimensional procedure, which consistently introduce coordinates and
momenta in the corresponding four-dimensional phase space, via a Hamiltonian
approach. For the one particle case, the starting point is a de Sitter momentum
space in five dimensions, with an additional constraint selected to recover the
mass shell condition in four dimensions. Different basis of DSR can be
recovered by selecting specific gauges to define the reduced four dimensional
degrees of freedom. This is shown for the Snyder basis in the one particle
case. We generalize the method to the many particles case and apply it again to
this basis. We show that the energy and momentum of the system, given by the
dynamical variables that are generators of translations in space and time and
which close the Poincar\'e algebra, are additive magnitudes. From this it
results that the rest energy (mass) of a composite object does not have an
upper limit, as opposed to a single component particle which does.Comment: 12 pages, no figures, AIP Conf. Pro
- …