Mon, 25 Nov 2019

16:00 - 17:00
L1

Regularity of minimisers for a model of charged droplets

Jonas Hirsh
(Universität Leipzig)
Further Information

Note the change of room

Abstract

We investigate properties of minimisers of a variational model describing the shape of charged liquid droplets. Roughly speaking, the shape of a charged liquid droplet is determined by the competition between an ”aggerating” term, due to surface tension forces, and to a ”disaggergating” term due to the repulsive effect between charged particles.

In my talk I want to present our ”first” analysis of the so called Deby-Hückel-type free energy. In particular we show that minimisers satisfy a partial regularity result, a first step of understanding the further properties of a minimiser. The presented results are joint work with Guido De Philippis and Giulia Vescovo.

 

Wed, 07 Mar 2018

14:00 - 15:00
L4

Uniform energy distribution for a non-local isoperimetric problem

Katarína Bellová
(Universität Leipzig)
Abstract

For energy functionals composed of competing short- and long-range interactions, minimizers are often conjectured to form essentially periodic patterns on some intermediate lengthscale. However,  not many detailed structural results or proofs of periodicity are known in dimensions larger than 1. We study a functional composed of  the attractive, local interfacial energy of charges concentrated on a hyperplane and the energy of the electric field generated by these charges in the full space, which can be interpreted as a repulsive, non-local functional of the charges. We follow the approach of Alberti-Choksi-Otto and prove that the energy of minimizers of this functional is uniformly distributed  on cubes intersecting the hyperplane, which are sufficiently large with respect to the intrinsic lengthscale.

This is a joint work with A. Julia and F. Otto.

Mon, 02 May 2016

16:00 - 17:00
L4

Square Functions and the Muckenhoupt Weight Classes of Elliptic Measures

Bernd Kirchheim
(Universität Leipzig)
Abstract

We give a new characterization of the property that the elliptic measure
belongs to the infinity weight Muckenhoupt class
in terms of a Carleson measure property of bounded solutions.
This is joint work with C.Kenig, J.Pipher and T.Toro

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