A link for this talk will be sent to our mailing list a day or two in advance. If you are not on the list and wish to be sent a link, please contact Benjamin Fehrman.
I will discuss regularity properties for solutions of linear second order non-uniformly elliptic equations in divergence form. Assuming certain integrability conditions on the coefficient field, we obtain local boundedness and validity of Harnack inequality. The assumed integrability assumptions are sharp and improve upon classical results due to Trudinger from the 1970s.
As an application of the local boundedness result, we deduce a quenched invariance principle for random walks among random degenerate conductances. If time permits I will discuss further regularity results for nonlinear non-uniformly elliptic variational problems.
- PDE CDT Lunchtime Seminar