Topics in the Dean-Kawasaki model, Federico Cornalba (Bath)
TBC
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 »
Rigidity and flatness of the image of 2-dimensional ∞-harmonic maps, Hussien Abugirda (Reading)
Hussien Ali Hussien Abugirda abstract
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 »
A variational problem in L∞ involving the Laplacian, Roger Moser (Bath)
A variational problem in L∞ involving the Laplacian
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 »
Convex combinations and rearrangements of solutions to elliptic and parabolic equations, Paolo Salani (Florence)
I will describe a method which allows to compare solutions of different elliptic and parabolic equations in different domains. As a by-product, it is possible to define a new type of rearrangement which applies to equations not necessarily in divergence form, leading to Talenti type results. In the case of variational problems, the method applies… Read More »
Characterisation of the PDE system of vectorial Calculus of vari- ations in L∞ via affine variations. Birzhan Ayanbayev (Reading)
b-ayanbayev-abstract
Existence of 1D Vectorial Absolute Minimisers in L∞ under Minimal Assumptions. Hussien Abugirda (Reading)
h-abugirda-abstract
Analytical and numerical aspects of a gradient-flow-description for zero-range-processes. Peter Embacher (Cardiff)
Recent work on a description of zero-range-processes as entropy-driven gradient-flows is presented. Special emphasis is layed on how this can be exploited for numerically finding the corresponding thermodynamic metric of the process.