Nonlinear elastic free energies and gradient Young- Gibbs measures
Kotecky, Roman and Luckhaus, S.. Nonlinear elastic free energies and gradient Young- Gibbs measures. Communications in Mathematical Physics . ISSN 1432-0916 (In Press)Full text not available from this repository.
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We investigate, in a fairly general setting, the limit of large volume equilibrium Gibbs measures for elasticity type Hamiltonians with clamped boundary conditions. The existence of a quasiconvex free energy, forming the large deviations rate functional, is shown using a new interpolation lemma for partition functions. The local behaviour of the Gibbs measures can be parametrized by Young measures on the space of gradient Gibbs measures. In view of unboundedness of the state space, the crucial tool here is an exponential tightness estimate that holds for a vast class of potentials and the construction of suitable compact sets of gradient Gibbs measures.
|Item Type:||Journal Article|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||Communications in Mathematical Physics|
|Publication Status:||In Press|
|Access rights to Published version:||Restricted or Subscription Access|
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