Nonlinear Elastic Free Energies and Gradient Young-Gibbs Measures
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 l...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kotecký, Roman [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2014 |
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| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Springer Berlin Heidelberg, 1965, 326(2014), 3 vom: 22. Feb., Seite 887-917 |
|---|---|
| Übergeordnetes Werk: |
volume:326 ; year:2014 ; number:3 ; day:22 ; month:02 ; pages:887-917 |
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| DOI / URN: |
10.1007/s00220-014-1903-6 |
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OLC2038906025 |
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| 520 | |a 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. | ||
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10.1007/s00220-014-1903-6 doi (DE-627)OLC2038906025 (DE-He213)s00220-014-1903-6-p DE-627 ger DE-627 rakwb eng 530 510 VZ Kotecký, Roman verfasserin aut Nonlinear Elastic Free Energies and Gradient Young-Gibbs Measures 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2014 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. Free Energy Radon Partition Function Topological Space Weak Topology Luckhaus, Stephan aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 326(2014), 3 vom: 22. Feb., Seite 887-917 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:326 year:2014 number:3 day:22 month:02 pages:887-917 https://doi.org/10.1007/s00220-014-1903-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 326 2014 3 22 02 887-917 |
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10.1007/s00220-014-1903-6 doi (DE-627)OLC2038906025 (DE-He213)s00220-014-1903-6-p DE-627 ger DE-627 rakwb eng 530 510 VZ Kotecký, Roman verfasserin aut Nonlinear Elastic Free Energies and Gradient Young-Gibbs Measures 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2014 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. Free Energy Radon Partition Function Topological Space Weak Topology Luckhaus, Stephan aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 326(2014), 3 vom: 22. Feb., Seite 887-917 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:326 year:2014 number:3 day:22 month:02 pages:887-917 https://doi.org/10.1007/s00220-014-1903-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 326 2014 3 22 02 887-917 |
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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. © Springer-Verlag Berlin Heidelberg 2014 |
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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. © Springer-Verlag Berlin Heidelberg 2014 |
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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. © Springer-Verlag Berlin Heidelberg 2014 |
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10.1007/s00220-014-1903-6 |
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