Operator-norm convergence estimates for elliptic homogenisation problems on periodic singular structures

2018/01/06 by Kirill Cherednichenko, Cherednichenko, Kirill, Serena D'Onofrio +1
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.1801.02097

16 pages

arxiv created 2021/02/15 · arxiv updated 2021/02/16

Abstract

For a an arbitrary periodic Borel measure μ, we prove order O(ε) operator-norm resolvent estimates for the solutions to scalar elliptic problems in L²(\mathbb R^d, dμ^ε) with ε-periodic coefficients, ε>0. Here μ^ε is the measure obtained by ε-scaling of μ. Our analysis includes both the case of a measure absolutely continuous with respect to the standard Lebesgue measure and the case of "singular" periodic structures (or "multistructures"), when μ is supported by lower-dimensional manifolds.

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