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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.… Click to show full 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.
Keywords:
estimates elliptic;
norm convergence;
convergence estimates;
measure;
operator norm;
problems periodic
Journal Title: Journal of Mathematical Sciences
Year Published: 2018
Link to full text (if available)
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Journal Title: Journal of Mathematical Sciences
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!