TY - JOUR
T1 - A global method for deterministic and stochastic homogenisation in BV
AU - Cagnetti, Filippo
AU - Dal Maso, Gianni
AU - Scardia, Lucia
AU - Zeppieri, Caterina Ida
N1 - 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 Probabilità 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 Münster: 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:
© 2022, The Author(s).
PY - 2022/6
Y1 - 2022/6
N2 - 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.
AB - 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.
KW - Blow-up method
KW - Free-discontinuity problems
KW - Stochastic homogenisation
KW - Γ -convergence
UR - http://www.scopus.com/inward/record.url?scp=85127939577&partnerID=8YFLogxK
U2 - 10.1007/s40818-022-00119-4
DO - 10.1007/s40818-022-00119-4
M3 - Article
C2 - 35465087
AN - SCOPUS:85127939577
SN - 2524-5317
VL - 8
JO - Annals of PDE
JF - Annals of PDE
IS - 1
M1 - 8
ER -