相关论文: Equilibrium measures for higher dimensional rotati…
Apart from the flat space with an angular deficit, Einstein general relativity possesses another cylindrically symmetric solution. Because this configuration displays circles whose "circumferences" tend to zero when their "radius" go to…
Given a domain D in R^d with mild geometric measure theoretic assumptions on its boundary, we show that boundedness of the principal value Riesz tranforms (witn kernel of homogeneity -(d-1)) on H\"older spaces of order alpha on the boundary…
As was recently shown in Ref. 1, many eigenstates of a random Rydberg gas with resonant dipole-dipole interactions are highly delocalized. Although the high degree of delocalization is generic to various types of power-law interactions and…
In this paper we develop a new set of results based on a nonlocal gradient jointly inspired by the Riesz s-fractional gradient and Peridynamics, in the sense that its integration domain depends on a ball of radius delta > 0 (horizon of…
We investigate generalized liquid drop models with screened Riesz-type interactions, focusing in particular on truncated Coulomb and Yukawa potentials in three dimensions. While the classical Gamow model with Coulomb interaction is…
In this paper, we characterize the rectifiability (both uniform and not) of an Ahlfors regular set, E, of arbitrary co-dimension by the behavior of a regularized distance function in the complement of that set. In particular, we establish a…
In this article, we look for the weight functions (say $g$) that admits the following generalized Hardy-Rellich type inequality: $ \int_{\Omega} g(x) u^2 dx \leq C \int_{\Omega} |\Delta u|^2 dx, \forall u \in \mathcal{D}^{2,2}_0(\Omega), $…
In this work, we study the Wasserstein gradient flow of the Riesz energy defined on the space of probability measures. The Riesz kernels define a quadratic functional on the space of measure which is not in general geodesically convex in…
We consider a classical system of n charged particles in an external confining potential, in any dimension d larger than 2. The particles interact via pairwise repulsive Coulomb forces and the coupling parameter scales like the inverse of n…
We present new method for studying the equilibrium properties of interacting fluids in an arbitrary external filed. The method is valid in any dimension and it yields an exact results in one dimension. Using this approach, we derive a…
We investigate a family of radially symmetric Coulomb gas systems at inverse temperature $\beta = 2$. The family is characterised by the property that the density of the equilibrium measure vanishes on a ring at radius $r_*$, which lies…
Inequalities for Riesz potentials are well-known to be equivalent to Sobolev inequalities of the same order for domain norms ``far" from $L^1$, but to be weaker otherwise. Recent contributions by Van Schaftingen, by Hernandez, Rai\c{t}\u{a}…
We prove several results for the Coulomb gas in any dimension $d \geq 2$ that follow from isotropic averaging, a transport method based on Newton's theorem. First, we prove a high-density Jancovici-Lebowitz-Manificat law, extending the…
Using the wave equation in d > or = 1 space dimensions it is illustrated how dynamical equations may be simultaneously Poincar\'e and Galileo covariant with respect to different sets of independent variables. This provides a method to…
There have been, over the last 8 years, a number of far reaching extensions of the famous original F. and M. Riesz's uniqueness theorem that states that if a bounded analytic function in the unit disc of the complex plane $\Bbb C$ has the…
The gas of the interacted electrons is usually described within Kohn-Sham approximation by the set of Poisson and Schr\"{o}dinger equations with an effective potential for the single-particle wave functions. The solution of these equations…
This paper concerns the study of the incompressible Euler equations with variable density, in the case of space dimension $d=2$. Contrarily to their homogeneous (constant density) counterpart, those equations are not known to be well-posed…
Outer product frames are important objects in Hilbert space frame theory. But very little is known about them. In this paper, we make the first detailed study of the family of outer product frames induced directly by vector sequences. We…
We study the distribution of the position of the rightmost particle $x_{\max}$ in a $N$-particle Riesz gas in one dimension confined in a harmonic trap. The particles interact via long-range repulsive potential, of the form $r^{-k}$ with…
It is well-known that measures whose density is the form $e^{-V}$ where $V$ is a uniformly convex potential on $\RR^n$ attain strong concentration properties. In search of a notion of log-concavity on the discrete hypercube, we consider…