分野別セミナー

講演要旨：
We will be interested in C$^1$ globally defined and periodic
functions $u$ which satisfy $H(x,d_xu)\leq c$ everywhere with the
smallest possible $c$. These are called critical
subsolutions. Usually there does not exist C$^2$ critical
subsolutions. We will explain how Denjoy theory puts in two
dimensions strong restrictions on the existence of smoother
critical subsolutions. We will also show that (in all dimensions)
the obstruction to find smoother subsolutions is localized at the
neighborhood of the Aubry set.