Jean Dolbeault

TL;DR: In this article, the Hardy inequality was improved to a nonlinear integral quantity with super-quadratic growth, which is computed with respect to an inverse square weight, is controlled by the energy.

TL;DR: In this article, the existence and uniqueness of the solutions to the Cauchy problem and on the regularization properties (hypercontractivity and ultracontractivity) of the equation using the Lp-Euclidean logarithmic Sobolev inequality were investigated.

TL;DR: In this article, the authors studied the continuity of the time derivative of the solution to the one-dimensional parabolic obstacle problem with variable coefficients and proved that the solution is continuous for almost every time.

TL;DR: In this paper, the authors study variants of the SEIR model for interpreting some qualitative features of the statistics of the Covid-19 epidemic in France and propose a possible explanation that lockdown is creating social heterogeneity: even if a large majority of the population complies with the lockdown rules, a small fraction of population still has to maintain a normal or high level of social interactions.

TL;DR: In this paper, the rate of convergence towards a unique stationary state in self-similar variables, which describes the intermediate asymptotics of the solutions in the original variables, was studied.