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Communications in Mathematical Physics

, Volume 326, Issue 3, pp 887–917 | Cite as

Nonlinear Elastic Free Energies and Gradient Young-Gibbs Measures

  • Roman KoteckýEmail author
  • Stephan Luckhaus
Article

Abstract

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 the 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.

Keywords

Free Energy Radon Partition Function Topological Space Weak Topology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WarwickCoventryUK
  2. 2.Charles UniversityPragueCzech Republic
  3. 3.Institut für MathematikLeipzig UniversityLeipzigGermany

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