Geodesic
Non-Markovian quadratic forms obtained by homogenization
Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 2, pp. 323-337

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This paper is devoted to the asymptotic behaviour of quadratic forms defined on $L^{2}$. More precisely we consider the $\Gamma$-convergence of these functionals for the $L^{2}$-weak topology. We give an example in which some limit forms are not Markovian and hence the Beurling-Deny representation formula does not hold. This example is obtained by the homogenization of a stratified medium composed of insulating thin-layers. 
@article{BUMI_2003_8_6B_2_a3,
     author = {Briane, Marc},
     title = {Non-Markovian quadratic forms obtained by homogenization},
     journal = {Bollettino della Unione matematica italiana},
     pages = {323--337},
     publisher = {mathdoc},
     volume = {Ser. 8, 6B},
     number = {2},
     year = {2003},
     zbl = {1150.35009},
     mrnumber = {MR1988208},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_2_a3/}
}
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Briane, Marc. Non-Markovian quadratic forms obtained by homogenization. Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 2, pp. 323-337. http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_2_a3/