2,744 research outputs found
A shape optimization problem for Steklov eigenvalues in oscillating domains
In this paper we study the asymptotic behavior of some optimal design
problems related to nonlinear Steklov eigenvalues, under irregular (but
diffeomorphic) perturbations of the domain.Comment: Some typos fixe
Existence of solution to a critical equation with variable exponent
In this paper we study the existence problem for the Laplacian
operator with a nonlinear critical source. We find a local condition on the
exponents ensuring the existence of a nontrivial solution that shows that the
Pohozaev obstruction does not holds in general in the variable exponent
setting. The proof relies on the Concentration--Compactness Principle for
variable exponents and the Mountain Pass Theorem
Variational description of Gibbs-non-Gibbs dynamical transitions for spin-flip systems with a Kac-type interaction
We continue our study of Gibbs-non-Gibbs dynamical transitions. In the
present paper we consider a system of Ising spins on a large discrete torus
with a Kac-type interaction subject to an independent spin-flip dynamics
(infinite-temperature Glauber dynamics). We show that, in accordance with the
program outlined in \cite{vEFedHoRe10}, in the thermodynamic limit
Gibbs-non-Gibbs dynamical transitions are \emph{equivalent} to bifurcations in
the set of global minima of the large-deviation rate function for the
trajectories of the empirical density \emph{conditional} on their endpoint.
More precisely, the time-evolved measure is non-Gibbs if and only if this set
is not a singleton for \emph{some} value of the endpoint. A partial description
of the possible scenarios of bifurcation is given, leading to a
characterization of passages from Gibbs to non-Gibbs and vice versa, with sharp
transition times.
Our analysis provides a conceptual step-up from our earlier work on
Gibbs-non-Gibbs dynamical transitions for the Curie-Weiss model, where the
mean-field interaction allowed us to focus on trajectories of the empirical
magnetization rather than the empirical density.Comment: Key words and phrases: Curie-Weiss model, Kac model, spin-flip
dynamics, Gibbs versus non-Gibbs, dynamical transition, large deviation
principles, action integral, bifurcation of rate functio
An optimization problem for the first weighted eigenvalue problem plus a potential
In this paper, we study the problem of minimizing the first eigenvalue of the
Laplacian plus a potential with weights, when the potential and the weight
are allowed to vary in the class of rearrangements of a given fixed potential
and weight . Our results generalized those obtained in [9] and [5].Comment: 15 page
A mass transportation approach for Sobolev inequalities in variable exponent spaces
In this paper we provide a proof of the Sobolev-Poincar\'e inequality for
variable exponent spaces by means of mass transportation methods. The
importance of this approach is that the method is exible enough to deal with
different inequalities. As an application, we also deduce the Sobolev-trace
inequality improving the result obtained by Fan.Comment: 12 page
La situación de Levante en el Estrecho.
Sin resume
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