Analysis Seminar

We present a purely variational approach to the regularity theory for the Monge-Ampère equation, or rather optimal transportation, introduced with M. Goldman. Following De Giorgi’s philosophy for the regularity theory of minimal surfaces, it is...

Consider a (possibly time-dependent) vector field $v$ on the Euclidean space. The classical Cauchy-Lipschitz (also named Picard-Lindel\"of) Theorem states that, if the vector field $v$ is Lipschitz in space, for every initial datum $x$ there is a...

We provide geometric sufficient conditions for Reifenberg flat sets of any integer dimension in Euclidean space to be parametrized by a Lipschitz map with Hölder derivatives. The conditions use a Jones type square function and all statements are...

Some words in the title are between quotation marks because it is a matter of interpretation. For dynamical systems on finite dimensional spaces, one often equates observable events with positive Lebesgue measure sets, and invariant distributions...

Given a planar domain with sufficiently regular boundary, one can study periodic orbits of the associated billiard problem. Periodic orbits have a rich and quite intricate structure and it is natural to ask how much information about the domain is...

Flocking and swarming models which seek to explain pattern formation in mathematical biology often assume that organisms interact through a force which is attractive over large distances yet repulsive at short distances. Suppose this force is given...

In the talk we will focus on certain constructions of weak solutions to the Navier--Stokes inequality (NSI), \[ u \cdot \left( u_t - \nu \Delta + (u\cdot \nabla ) u+ \nabla p \right) \leq 0\] on $\mathbb R^3$. Such vector fields satisfy both the...

Due to its importance in materials science where it models the slow relaxation of grain boundaries, multiphase mean curvature flow has received a lot of attention over the last decades.

In this talk, I want to present two theorems. The first one is...