In this talk I will present a stochastic homogenization result for
free-discontinuity functionals. Assuming stationarity for the random volume
and surface integrands, we prove the existence of a homogenized 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 realization and the pointwise Subadditive
Ergodic Theorem by Akcoglou and Krengel, we characterize the limit volume
and surface integrands in terms of asymptotic cell formulas. Our
homogenization result extends to the SBV-setting the classical qualitative
results by Papanicolaou and Varadhan, Kozlov, and Dal Maso and Modica,
which were formulated in the Sobolev setting. Some recent developments
obtained in the BV setting will be also addressed.
Joint work with F. Cagnetti (Sussex) , G. Dal Maso (SISSA), and L. Scardia
(Heriot-Watt)
Angelegt am Friday, 16.04.2021 14:20 von Sebastian Throm
Geändert am Friday, 04.06.2021 11:01 von Sebastian Throm
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