Suppose that we want to minimise the L-infinity norm of the Laplacian of a function (or a similar quantity) under Dirichlet boundary conditions. This is a convex, but not strictly convex variational problem. Nevertheless, it turns out that it has a unique solution, which is characterised by a system of PDEs. The behaviour is thus quite different from the better-known first order problems going back to Aronsson. This is joint work with N. Katzourakis (Reading).
- Partial Differential Equations Seminar