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We show that the Hamiltonian action satisfies the Palais-Smale condition overa "mixed regularity" space of loops in cotangent bundles, namely the space ofloops with regularity $H^s$, $s\in (\frac 12, 1)$, in the base and $H^{1-s}$ inthe fiber direction. As an application, we give a simplified proof of a theoremof Hofer-Viterbo on the existence of closed characteristic leaves for certaincontact type hypersufaces in cotangent bundles.

The Palais-Smale condition for the Hamiltonian action on a mixed regularity space of loops in cotangent bundles and applications