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Article Dans Une Revue Communications in Partial Differential Equations Année : 2019

On correctors for linear elliptic homogenization in the presence of local defects

Résumé

We consider the corrector equation associated, in homogenization theory , to a linear second-order elliptic equation in divergence form −∂i(aij∂ju) = f , when the diffusion coefficient is a locally perturbed periodic coefficient. The question under study is the existence (and uniqueness) of the corrector, strictly sublinear at infinity, with gradient in L r if the local perturbation is itself L r , r < +∞. The present work follows up on our works [7, 8, 9], providing an alternative, more general and versatile approach , based on an a priori estimate, for this well-posedness result. Equations in non-divergence form such as −aij∂iju = f are also considered, along with various extensions. The case of general advection-diffusion equations −aij∂iju + bj∂ju = f is postponed until our future work [10]. An appendix contains a corrigendum to our earlier publication [9].
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Dates et versions

hal-01697104 , version 1 (30-01-2018)

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Xavier Blanc, Claude Le Bris, Pierre Louis Lions. On correctors for linear elliptic homogenization in the presence of local defects. Communications in Partial Differential Equations, 2019, ⟨10.1080/03605302.2018.1484764⟩. ⟨hal-01697104⟩
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