Operator-Norm Convergence Estimates for Elliptic Homogenization Problems on Periodic Singular Structures
- Authors: Cherednichenko K.1, D’Onofrio S.1
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Affiliations:
- University of Bath
- Issue: Vol 232, No 4 (2018)
- Pages: 558-572
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241354
- DOI: https://doi.org/10.1007/s10958-018-3887-9
- ID: 241354
Cite item
Abstract
For an arbitrary periodic Borel measure μ we prove order O(ε) operator-norm resolvent estimates for the solutions to scalar elliptic problems in L2(ℝd, dμε) with ε-periodic coefficients, ε > 0. Here, με is the measure obtained by ε-scaling of μ. Our analysis includes the case of a measure absolutely continuous with respect to the standard Lebesgue measure, as well as the case of “singular” periodic structures (or “multistructures”), when μ is supported by lower-dimensional manifolds.
About the authors
K. Cherednichenko
University of Bath
Author for correspondence.
Email: k.cherednichenko@bath.ac.uk
United Kingdom, Claverton Down, Bath, BA2 7AY
S. D’Onofrio
University of Bath
Email: k.cherednichenko@bath.ac.uk
United Kingdom, Claverton Down, Bath, BA2 7AY