Existence, uniqueness and regularity of the minimizer of energy related to perimeter minus fractional perimeter

Abstract: We are interested in the asymptotic behaviors of the following energy functional $E(\Omega)=\sigma Per(\Omega)+\beta V_K(\Omega)$ defined for $|\Omega|=m$. Here the perimeter tries to keep the mass together in a ball, and $V_K$ is a non-local repulsive interaction energy trying to spread the mass around. We will then discuss the existence, uniqueness snd regularity properties of the minimizers of the energy especially in the regime where the energy $E(\Omega)$ converges to Perimeter minus fractional perimeter.

analysis of PDEsclassical analysis and ODEs

Audience: researchers in the topic

HA-GMT-PDE Seminar

Series comments: Description: A senior graduate student/postdoc series in harmonic analysis, geometric measure theory, and partial differential equations.

Meetings will be weekly, and usually will occur on Monday, with some exceptions. For each talk, the Zoom link is made available in the website too. Contact Bruno Poggi at poggi008@umn.edu if you would like to subscribe to the seminar mailing list.