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

Luca Asselle; Maciej Starostka

doi:10.1007/s00526-020-01762-0

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

Abstract

We show that the Hamiltonian action satisfies the Palais-Smale condition over a “mixed regular- ity” space of loops in cotangent bundles, namely the space of loops with regularity H^s, s ∈ (1/2, 1), in the baseand H^{1−s} in the fiber direction. As an application, we give a simplified proof of a theorem of Hofer-Viterbo on the existence of closed characteristic leaves for certain contact type hypersufaces in cotangent bundles.

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Authors (2)

Luca Asselle Dr
Maciej Starostka dr inż.

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DOI:: Digital Object Identifier (open in new tab) 10.1007/s00526-020-01762-0
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Keywords

HAMILTONIAN ACTION FUNCTIONAL, PALAIS-SMALE CONDITION, WEINSTEIN CONJECTURE

Details

Category:: Articles
Type:: artykuły w czasopismach
Published in:: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS no. 59, pages 1 - 28,
ISSN: 0944-2669
Language:: English
Publication year:: 2020
Bibliographic description:: Asselle L., Starostka M.: The Palais–Smale condition for the Hamiltonian action on a mixed regularity space of loops in cotangent bundles and applications// CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS -Vol. 59,iss. 4 (2020), s.1-28
DOI:: Digital Object Identifier (open in new tab) 10.1007/s00526-020-01762-0
Verified by:: Gdańsk University of Technology