Stochastic Homogenisation of Free-Discontinuity Problems
Stochastic Homogenisation of Free-Discontinuity Problems
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DOI：
10.1007/s00205-019-01372-x
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发表时间：
2019-08-01
影响因子：
2.5
通讯作者：
Zeppieri, Caterina Ida
中科院分区：
文献类型：
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作者：
Cagnetti, Filippo;Dal Maso, Gianni;Zeppieri, Caterina Ida
本文研究了自由不连续泛函的随机均匀化问题。假设随机体积积分和随机曲面积分的平稳性，我们证明了均匀化随机自由不连续泛函的存在性，它在遍历情况下是确定的。此外，通过建立泛函在任意固定点的确定性收敛性与Akcoglou和Krengel的点向次加性遍历定理之间的联系，我们用渐近单元格公式描述了极限体积和表面积分。
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.