Holder continuity of weak solutions to infinitely degenerate elliptic equations

Lyudmila Korobenko
University of Pennsylvania
Wednesday, May 3, 2017 -
3:35pm to 4:35pm
VinH 211

I will talk about local boundedness and Ho?lder continuity of weak solutions to
certain infinitely degenerate elliptic divergence form equations. We have previously
shown local boundedness and continuity of weak solutions for certain classes of
degeneracies in 2 and 3 dimensions, using Moser iteration scheme. The boundedness
result we obtained was not sharp, and it was not known if weak solutions are
bounded for a bigger class of degeneracies, which we called a “Moser gap”. Using
the truncation method of DeGiorgi iteration we prove local boundedness in the
gap left open by Moser iteration. Moreover, for homogeneous equations we show
Ho?lder continuity for the same range of degeneracies. These results are sharp in
dimensions n ? 3.