Stochastic Homogenisation of Free-Discontinuity Problems

In this paper we study the stochastic homogenisation of free-discontinuity functionals . Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which is deterministic in the ergodic case. Moreover, by establis...

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Veröffentlicht in:Archive for rational mechanics and analysis Jg. 233; H. 2; S. 935 - 974
Hauptverfasser: Cagnetti, Filippo, Dal Maso, Gianni, Scardia, Lucia, Zeppieri, Caterina Ida
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2019
Springer Nature B.V
Schlagworte:
Classical Mechanics
Complex Systems
Discontinuity
Ergodic processes
Fluid- and Aerodynamics
Homogenization
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
ISSN:0003-9527, 1432-0673
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Zusammenfassung:In this paper we study the stochastic homogenisation of free-discontinuity functionals . Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which is deterministic in the ergodic case. Moreover, by establishing a connection between the deterministic convergence of the functionals at any fixed realisation and the pointwise Subadditive Ergodic Theorem by Akcoglou and Krengel, we characterise the limit volume and surface integrands in terms of asymptotic cell formulas.
Bibliographie:ObjectType-Article-1
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ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-019-01372-x