Corpus ID: 221139712

Sharp stability for the interaction energy

@article{Yan2020SharpSF,
  title={Sharp stability for the interaction energy},
  author={Xukai Yan and Yao Yao},
  journal={arXiv: Analysis of PDEs},
  year={2020}
}
This paper is devoted to stability estimates for the interaction energy with strictly radially decreasing interaction potentials, such as the Coulomb and Riesz potentials. For a general density function, we first prove a stability estimate in terms of the $L^1$ asymmetry of the density, extending some previous results by Burchard-Chambers, Frank-Lieb and Fusco-Pratelli for characteristic functions. We also obtain a stability estimate in terms of the 2-Wasserstein distance between the density… Expand

Figures from this paper

Some minimization problems for mean field models with competing forces
  • Rupert L. Frank
  • Mathematics, Physics
  • 2021
We review recent results on three families of minimization problems, defined on subsets of nonnegative functions with fixed integral. The competition between attractive and repulsive forces leads toExpand

References

SHOWING 1-10 OF 26 REFERENCES
On minimizers of interaction functionals with competing attractive and repulsive potentials
Abstract We consider a family of interaction functionals consisting of power-law potentials with attractive and repulsive parts and use the concentration compactness principle to establish theExpand
A stability result for Riesz potentials in higher dimensions
We prove a stability estimate, with the optimal quadratic error term, for the Coulomb energy of a set in $\mathbb{R}^n$ with $n \geq 3$. This estimate extends to a range of Riesz potentials.
A Convexity Principle for Interacting Gases
A new set of inequalities is introduced, based on a novel but natural interpolation between Borel probability measures on R d . Using these estimates in lieu of convexity or rearrangementExpand
Extended Rearrangement Inequalities and Applications to Some Quantitative Stability Results
In this paper, we prove a new functional inequality of Hardy–Littlewood type for generalized rearrangements of functions. We then show how this inequality provides quantitative stability results ofExpand
Publisher Correction to: Isodiametry, Variance, and Regular Simplices from Particle Interactions
Consider a pressureless gas interacting through an attractive-repulsive potential given as a difference of power laws and normalized so that its unique minimum occurs at unit separation. For a rangeExpand
Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies
We obtain a sharp quantitative isoperimetric inequality for nonlocal s-perimeters, uniform with respect to s bounded away from 0. This allows us to address local and global minimality properties ofExpand
Sharp stability for the Riesz potential
In this paper we show the stability of the ball as maximizer of the Riesz potential among sets of given volume. The stability is proved with sharp exponent $1/2$, and is valid for any dimensionExpand
Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
The equation dealt with in this paper is in three dimensions. It comes from minimizing the functional which, in turn, comes from an approximation to the Hartree-Fock theory of a plasma. It describesExpand
Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media
An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particlesExpand
Stability for the Brunn-Minkowski and Riesz Rearrangement Inequalities, with Applications to Gaussian Concentration and Finite Range Non-local Isoperimetry
Abstract We provide a simple, general argument to obtain improvements of concentration-type inequalities starting from improvements of their corresponding isoperimetric-type inequalities. We applyExpand
...
1
2
3
...