Speaker
Lukas Koch
(MPI for MiS, Leipzig)
Description
I will recall the classical theory of convex duality and explain how this can be used to obtain regularity statements in the study of minimisers of the problem
$$\mathrm{min}_{u\in W^{1,p}(\Omega)}\int_\Omega F(x,\mathrm{D} u)\mathrm{d} x.$$
In particular, I will comment on recent results obtained in collaboration with Cristiana de Filippis (Parma) and Jan Kristensen (Oxford) concerning the validity of the Euler–Lagrange equations for extended real-valued integrands $F$ satisfying no upper growth condition as well as concerning integrands $F$ satisfying controlled duality $(p,q)$-growth. The main example of integrands $F$ satisfying controlled duality $(p,q)$-growth are convex polynomials.
