Sharp stability for the interaction energy

Abstract: For a nonnegative density f and radially decreasing interaction potential W, the interaction energy is given by E[f]= \int f(x)f(y)W(x-y) dxdy. The celebrated Riesz rearrangement inequality says that the interaction energy satisfies E[f] \le E[f^*], where f^* is the radially decreasing rearrangement of f. In this talk, I will discuss the quantitative estimate of this inequality. I will first make an introduction about the problem and describe some previous results about the stability estimate for characteristic functions. I will then present a recent work with Yao Yao, where we establish the stability estimate for general densities.

mathematical physicsanalysis of PDEsclassical analysis and ODEscategory theoryfunctional analysislogicoptimization and controlrepresentation theory

Audience: researchers in the topic

VCU ALPS (Analysis, Logic, and Physics Seminar)

Series comments: Description: Research seminar on topics ranging from analysis and logic to mathematical physics.

Meetings will be conducted over Zoom:

Meeting ID: 951 0562 0974

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