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2016 Limiting distribution of elliptic homogenization error with periodic diffusion and random potential
Wenjia Jing
Anal. PDE 9(1): 193-228 (2016). DOI: 10.2140/apde.2016.9.193

Abstract

We study the limiting probability distribution of the homogenization error for second order elliptic equations in divergence form with highly oscillatory periodic conductivity coefficients and highly oscillatory stochastic potential. The effective conductivity coefficients are the same as those of the standard periodic homogenization, and the effective potential is given by the mean. We show that the limiting distribution of the random part of the homogenization error, as random elements in proper Hilbert spaces, is Gaussian and can be characterized by the homogenized Green’s function, the homogenized solution and the statistics of the random potential. This generalizes previous results in the setting with slowly varying diffusion coefficients, and the current setting with fast oscillations in the differential operator requires new methods to prove compactness of the probability distributions of the random fluctuation.

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Wenjia Jing. "Limiting distribution of elliptic homogenization error with periodic diffusion and random potential." Anal. PDE 9 (1) 193 - 228, 2016. https://doi.org/10.2140/apde.2016.9.193

Information

Received: 8 June 2015; Revised: 8 October 2015; Accepted: 28 October 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1335.35313
MathSciNet: MR3461305
Digital Object Identifier: 10.2140/apde.2016.9.193

Subjects:
Primary: 35R60
Secondary: 60B12

Keywords: periodic and stochastic homogenization , probability measures on Hilbert space , Random field , weak convergence of probability distributions

Rights: Copyright © 2016 Mathematical Sciences Publishers

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