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Bridging the Gaps Oberseminar Analysis: Caterina Zeppieri (WWU): Stochastic homogenization of free-discontinuity problems

Wednesday, 09.06.2021 12:00 per ZOOM: Link to Zoom info

Mathematik und Informatik

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 sthrom
Geändert am Friday, 04.06.2021 11:01 von sthrom
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Bridging the Gaps Oberseminar Analysis'
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