Author Archives: swngsn_admin

Some new results on Lipschitz regularizing effect for Parabolic Equations, Vinh Nguyen (Cardiff)

It is well-known that the bounded solution of the heat equation for any continuous initial condition becomes Lipschitz continuous as soon as time is positive. We aim at extending this phenomenon to nonlinear parabolic equations. In literature, this was done requiring quite restrictive structures in first order term. Here, we relax these limitations and we… Read More »

Nonlinear elliptic PDEs and ergodic Mean Field Games, Ermal Feleqi (Cardiff)

I will talk about a class of quasilinear elliptic systems of PDEs consisting of $N$ Hamilton-Jacobi-Bellman equations coupled with $N$ Fokker-Planck equations, generalising to $N>1$ populations the PDEs for stationary Mean-Field Games first proposed by Lasry and Lions. I will describe a wide range of sufficient conditions for the  existence of solutions to these systems: … Read More »

Existence of geometric D-solutions to the Dirichlet problem for the Infinity-Laplacian which are critical points, Nikos Katzourakis (Reading)

The Infinity-Laplacian is a 2nd order nonlinear PDE system with discontinuous coefficients which arises in vectorial Calculus of Variations in L-Infinity when minimising the sup-norm of the gradient over a class of Lipschitz maps. In this talk I will discuss an existence result of appropriately defined “weak” solutions to the Dirichlet problem for a generalised Infinity-Laplacian… Read More »