We discuss a one-phase degenerate free boundary problem which
arises from the minimization of the so-called Alt-Phillips
functional. We establish partial regularity results for the free
boundary and discuss the rigidity of global minimizers when...
This lecture is devoted to a survey on explicit stability
results in Gagliardo-Nirenberg-Sobolev and logarithmic Sobolev
inequalities. Generalized entropy methods based on carré du champ
computations and nonlinear diffusion flows can be used for...
We consider general two-dimensional autonomous velocity fields
and prove that their mixing and dissipation features are limited to
algebraic rates. As an application, we consider a standard cellular
flow on a periodic box, and explore potential...
The Brascamp-Lieb inequality is a fundamental inequality in
analysis, generalizing more classical inequalities such as Holder's
inequality, the Loomis-Whitney inequality, and Young's convolution
inequality: it controls the size of a product of...
This talk will be about a ferromagnetic spin system called the
Blume-Capel model. It was introduced in the '60s to model an exotic
multi-critical phase transition observed in the magnetisation of
uranium oxide. Mathematically speaking, the model can...
Given a linear equation whose principal term is given by a
degenerate dispersive pseudo-differential operator, we provide a
framework for the construction of degenerating wave packet
solutions. As an application, we prove strong ill-posedness
for...
Solitons are particle-like solutions to dispersive evolution
equations whose shapes persist as time evolves. In some situations,
these solitons appear due to the balance between nonlinear effects
and dispersion, in other situations their existence...
