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Counterexamples for the fractal Schrödinger convergence problem with an Intermediate Space Trick
(2021-12-09)
We construct counterexamples for the fractal Schrödinger convergence problem by combining a fractal extension of Bourgain's counterexample and the intermediate space trick of Du--Kim--Wang--Zhang. We confirm that the same ...
Discrepancy of Minimal Riesz Energy Points
(2021-12-01)
We find upper bounds for the spherical cap discrepancy of the set of minimizers of the Riesz s-energy on the sphere Sd. Our results are based on bounds for a Sobolev discrepancy introduced by Thomas Wolff in an unpublished ...
Discrete Carleman estimates and three balls inequalities
(2021-10-16)
We prove logarithmic convexity estimates and three balls inequalities for discrete magnetic Schrödinger operators. These quantitatively connect the discrete setting in which the unique continuation property fails and the ...
Cavity Volume and Free Energy in Many-Body Systems
(2021-10-01)
Within this work, we derive and analyse an expression for the free energy of a single-species system in the thermodynamic limit in terms of a generalised cavity volume, that is exact in general, and in principle applicable ...
Pointwise Convergence over Fractals for Dispersive Equations with Homogeneous Symbol
(2021-08-24)
We study the problem of pointwise convergence for equations of the type
$i\hbar\partial_tu + P(D)u = 0$, where the symbol $P$ is real, homogeneous and non-singular.
We prove that for initial data $f\in H^s(\mathbb{R}^n)$ ...
Bilinear Spherical Maximal Functions of Product Type
(2021-08-12)
In this paper we introduce and study a bilinear spherical maximal function of product type in the spirit of bilinear Calderón–Zygmund theory. This operator is different from the bilinear spherical maximal function considered ...
Echo Chains as a Linear Mechanism: Norm Inflation, Modified Exponents and Asymptotics
(2021-07-30)
In this article we show that the Euler equations, when linearized around a low frequency perturbation to Couette flow, exhibit norm inflation in Gevrey-type spaces as time tends to infinity. Thus, echo chains are shown to ...
On a probabilistic model for martensitic avalanches incorporating mechanical compatibility
(2021-07-01)
Building on the work by Ball et al (2015 MATEC Web of Conf. 33 02008), Cesana and Hambly (2018 A probabilistic model for interfaces in a martensitic phase transition arXiv:1810.04380), Torrents et al (2017 Phys. Rev. E 95 ...
Double layered solutions to the extended Fisher–Kolmogorov P.D.E.
(2021-06-22)
We construct double layered solutions to the extended Fisher–Kolmogorov P.D.E., under the assumption that the set of minimal heteroclinics of the corresponding O.D.E. satisfies a separation condition. The aim of our work ...
Variation bounds for spherical averages
(2021-06-22)
We consider variation operators for the family of spherical means, with special emphasis on $L^p\to L^q$ estimates