Integrable elliptic PDEs
Beatrice Pelloni (Heriot-Watt)
Thursday 2nd February, 2017 16:00-17:00 Maths 522
In the last twenty years, a considerable body of work has been produced to deal with the challenge of solving boundary value problems for integrable PDEs in two variables. This has consolidated an approach proposed by Fokas, and now know as the Unified Transform, as a powerful method to analyse these problems. In particular, this method has opened up the possibility to study integrable elliptic PDEs, which include all classical linear elliptic PDEs but also the prototypical nonlinear model, the elliptic sine-Gordon equation.
I will briefly discuss the method in general, and then focus on the applications and results specifically for elliptic PDEs.