Craig Cowan

Optimal Transport theory emerged more than two centuries ago as an engineering problem posed by Gaspard Monge just before the French revolution. Its rich mathematical structure was first revealed by the Russian Nobel-prize winner Kantorovich during...

We derive a general Hardy inequality and show most Hardy inequalities can be seen as special cases of this inequality. In addition we characterize the improvements of this inequality and (time permitting) we show an application of this inequality to...

I will discuss recent results concerning the regularity of the extremal solution associated with fourth order nonlinear eigenvalue problems on general domains. We show that the extremal solution is bounded under various assumptions on the...