@article{303b1d6325c948148a8c3cf8e1dcdfd9,
title = "A global method for deterministic and stochastic homogenisation in BV",
abstract = "In this paper we study the deterministic and stochastic homogenisation of free-discontinuity functionals under linear growth and coercivity conditions. The main novelty of our deterministic result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Combining this result with the pointwise Subadditive Ergodic Theorem by Akcoglu and Krengel, we prove a stochastic homogenisation result, in the case of stationary random integrands. In particular, we characterise the limit integrands in terms of asymptotic cell formulas, as in the classical case of periodic homogenisation.",
keywords = "Blow-up method, Free-discontinuity problems, Stochastic homogenisation, Γ -convergence",
author = "Filippo Cagnetti and \{Dal Maso\}, Gianni and Lucia Scardia and Zeppieri, \{Caterina Ida\}",
note = "Funding Information: F. Cagnetti was supported by the EPSRC under the Grant EP/P007287/1 “Symmetry of Minimisers in Calculus of Variations”. The research of G. Dal Maso was partially funded by the European Research Council under Grant No. 290888 “Quasistatic and Dynamic Evolution Problems in Plasticity and Fracture”. G. Dal Maso is a member of the Gruppo Nazionale per l{\textquoteright}Analisi Matematica, la Probabilit{\`a} e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The work of C. I. Zeppieri was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) project 3160408400 and under the Germany Excellence Strategy EXC 2044-390685587, Mathematics M{\"u}nster: Dynamics–Geometry–Structure. Funding Information: F. Cagnetti was supported by the EPSRC under the Grant EP/P007287/1 ?Symmetry of Minimisers in Calculus of Variations?. The research of G. Dal Maso was partially funded by the European Research Council under Grant No. 290888 ?Quasistatic and Dynamic Evolution Problems in Plasticity and Fracture?. G. Dal Maso is a member of the Gruppo Nazionale per l?Analisi Matematica, la Probabilit? e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The work of C. I. Zeppieri was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) project 3160408400 and under the Germany Excellence Strategy EXC 2044-390685587, Mathematics M?nster: Dynamics?Geometry?Structure. Publisher Copyright: {\textcopyright} 2022, The Author(s).",
year = "2022",
month = jun,
doi = "10.1007/s40818-022-00119-4",
language = "English",
volume = "8",
journal = "Annals of PDE",
issn = "2524-5317",
publisher = "Springer",
number = "1",
}