Minimizers of Dirichlet functionals on the n-torus and the Weak KAM Theory

Gershon Wolansky

Given a probability measure $\mu$ on the $n-$torus $T^n$ and a rotation vector $k\in R^n$, we ask wether there exists a minimizer to the integral $\int_{T^n} |\gradϕ+k|^2 dμ$. This p…