Geodesic
Operator-Norm Resolvent Asymptotic Analysis of Continuous Media with High-Contrast Inclusions
Matematičeskie zametki, Tome 111 (2022) no. 3, pp. 375-392

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Using a generalization of the classical notion of Weyl $m$-function and related formulas for the resolvents of boundary-value problems, we analyze the asymptotic behavior of solutions to a “transmission problem” for a high-contrast inclusion in a continuous medium, for which we prove the operator-norm resolvent convergence to a limit problem of “electrostatic” type. In particular, our results imply the convergence of the spectra of high-contrast problems to the spectrum of the limit operator, with order-sharp convergence estimates. The approach developed in the paper is of a general nature and can thus be successfully applied in the study of other problems of the same type.
Keywords: extensions of symmetric operators, generalized boundary triples, boundary value problems, transmission problems. 
@article{MZM_2022_111_3_a4,
     author = {A. V. Kiselev and L. O. Silva and K. D. Cherednichenko},
     title = {Operator-Norm {Resolvent} {Asymptotic} {Analysis} of {Continuous} {Media} with {High-Contrast} {Inclusions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {375--392},
     publisher = {mathdoc},
     volume = {111},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_3_a4/}
}
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A. V. Kiselev; L. O. Silva; K. D. Cherednichenko. Operator-Norm Resolvent Asymptotic Analysis of Continuous Media with High-Contrast Inclusions. Matematičeskie zametki, Tome 111 (2022) no. 3, pp. 375-392. http://geodesic.mathdoc.fr/item/MZM_2022_111_3_a4/