Category Archives: Meeting 11

PDEs and probability – Horatio Boedihardjo

We will discuss the classical relationships between probability and PDEs, as well as some recent developments. In particular, we will explain our ongoing study of an eigenvalue problem associated with a linear matrix-valued elliptic PDE from probability theory. Joint work with Ni Hao (UCL).

Stochastic homogenisation of high-contrast media – Mikhail Cherdantsev

Using a suitable stochastic version of the compactness argument of V. V. Zhikov, we develop a probabilistic framework for the analysis of heterogeneous media with high contrast. We show that an appropriately defined multiscale limit of the field in the original medium satisfies a system of equations corresponding to the coupled “macroscopic” and “microscopic” components… Read More »

On the existence and uniqueness of vectorial absolute minimisers in Calculus of Variations in L-infinity – Nikos Katzourakis

Calculus of Variations in the space L-infinity has a relatively short history in Analysis. The scalar-valued theory was pioneered by the Swedish mathematician Gunnar Aronsson in the 1960s and since then has developed enormously. The general vector-valued case delayed a lot to be developed and its systematic development began in the 2010s. One of the… Read More »

Uniqueness of minimisers of Ginzburg-Landau functionals – Luc Nguyen

We provide necessary and sufficient conditions for the uniqueness of minimisers of the Ginzburg-Landau functional for $\RR^n$-valued maps under suitable convexity assumption on the potential and for $H^{1/2} \cap L^\infty$ boundary data that is non-negative in a fixed direction $e\in \SSphere^{n-1}$. Furthermore, we show that, when minimisers are non-unique, the set of minimisers is invariant… Read More »