Geodesic
Averaging of periodic elliptic differential operators with the account of a~corrector
Algebra i analiz, Tome 17 (2005) no. 6, pp. 1-104.

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M. Sh. Birman; T. A. Suslina. Averaging of periodic elliptic differential operators with the account of a~corrector. Algebra i analiz, Tome 17 (2005) no. 6, pp. 1-104. http://geodesic.mathdoc.fr/item/AA_2005_17_6_a0/

[Bal] Bakhvalov N. S., “Osrednennye kharakteristiki tel s periodicheskoi strukturoi”, Dokl. AN SSSR, 218:5 (1974), 1046–1048

[Ва2] Bakhvalov N. S., “Osrednenie differentsialnykh uravnenii s chastnymi proizvodnymi s bystro ostsilliruyuschimi koeffitsientami”, Dokl. AN SSSR, 221:3 (1975), 516–519 | MR | Zbl

[ВаРа] Bakhvalov N. S., Panasenko G. P., Osrednenie protsessov v periodicheskikh sredakh, Nauka, M., 1984, 352 pp. | MR | Zbl

[BeLP] Bensoussan A., Lions J.-L., Papanicolaou G., Asymptotic analysis for periodic structures, North-Holland Publishing Co., Amsterdam–New York, 1978, 700 pp. | MR

[В] Birman M. Sh., “O protsedure usredneniya dlya periodicheskikh operatorov v okrestnosti kraya vnutrennei lakuny”, Algebra i analiz, 15:4 (2003), 61–71 | MR | Zbl

[BSul] Birman M., Suslina T., “Threshold effects near the lower edge of the spectrum for periodic differential operators of mathematical physics”, Systems, Approximation, Singular Integral Operators, and Related Topics (Bordeaux, 2000), Oper. Theory Adv. Appl., 129, Birkhäuser, Basel, 2001, 71–107 | MR | Zbl

[BSu2] Birman M. Sh., Suslina T. A., “Periodicheskie differentsialnye operatory vtorogo poryadka. Porogovye svoistva i usredneniya”, Algebra i analiz, 15:5 (2003), 1–108 | MR | Zbl

[BSu3] Birman M. Sh., Suslina T. A., “Usrednenie mnogomernogo periodicheskogo ellipticheskogo operatora v okrestnosti kraya vnutrennei lakuny”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii 36, Zap. nauch. semin. POMI, 318, 2004, 60–74 | Zbl

[BSu4] Birman M. Sh. (joint work with T. A. Suslina), Homogenization of periodic differential operators in $\mathbb R^d$ as a spectral threshold effect, Report No. 53/2004, Spectral Analysis of Partial Differential Equations, November 28th–December 4th, Mathematisches Forschungsinstitut Oberwolfach, 2004, 2847–2849 | MR

[BSu5] Birman M. Sh., Suslina T. A., “Porogovye approksimatsii rezolventy faktorizovannogo samosopryazhennogo semeistva s uchetom korrektora”, Algebra i analiz, 17:5 (2005), 69–90 | MR

[COrV] Conca C., Orive R., Vanninathan M., “Bloch approximation in homogenization and applications”, SIAM J. Math. Anal., 33:5 (2002), 1166–1198 | DOI | MR | Zbl

[Gl] Griso G., “Error estimate and unfolding for periodic homogenization”, Asympt. Anal., 40 (2004), 269–286 | MR | Zbl

[G2] Griso G., “Interior error estimate for periodic homogenization”, C. R. Math. Acad. Sci. Paris, 340 (2005), 251–254 | MR | Zbl

[Zhl] Zhikov V. V., “Spektralnyi podkhod k asimptoticheskim zadacham diffuzii”, Differents. uravneniya, 25:1 (1989), 44–50 | MR | Zbl

[Zh2] Zhikov V. V., “Ob operatornykh otsenkakh v teorii usredneniya”, Dokl. RAN, 403:3 (2005), 305–308 | MR | Zbl

[Zh3] Zhikov V. V., “O spektralnom metode v teorii usredneniya”, Tr. Mat. in-ta RAN, 250, 2005, 95–104 | MR | Zbl

[Zh4] Zhikov V. V., “O nekotorykh otsenkakh iz teorii usredneniya”, Dokl. RAN, 406:5 (2006), 597–601 | MR | Zbl

[ZhKO] Zhikov V. V., Kozlov S. M., Oleinik O. A., Usrednenie differentsialnykh operatorov, Fizmatgiz, M., 1993, 464 pp. | MR | Zbl

[ZhPas] Zhikov V. V., Pastukhova S. E., “Ob operatornykh otsenkakh dlya nekotorykh zadach teorii usredneniya”, Russian J. Math. Phys., 12:4 (2005), 515–524 | MR | Zbl

[Ka] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

[Ma] Marcinkiewicz J., “Sur les multiplicateurs des series de Fourier”, Studia Math., 8 (1939), 78–91

[Mi] Mikhlin S. G., Mnogomernye singulyarnye integraly i integralnye uravneniya, Fizmatgiz, M., 1962 | MR | Zbl

[LU] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1964 | MR

[Pas] Pastukhova S. E., “O nekotorykh otsenkakh iz usredneniya zadach teorii uprugosti”, Dokl. RAN, 406:5 (2006), 604–608 | MR | Zbl

[Se] Sevostyanova E. V., “Asimptoticheskoe razlozhenie resheniya ellipticheskogo uravneniya vtorogo poryadka s periodicheskimi bystro ostsilliruyuschimi koeffitsientami”, Mat. sb., 115:2 (1981), 204–222 | MR

[Sul] Suslina T. A., “Ob usrednenii periodicheskoi sistemy Maksvella”, Funkts. anal. i ego pril., 38:3 (2004), 90–94 | MR | Zbl

[Su2] Suslina T. A., “Usrednenie statsionarnoi periodicheskoi sistemy Maksvella”, Algebra i analiz, 16:5 (2004), 162–244 | MR

[Su3] Suslina T. A., Usrednenie periodicheskikh parabolicheskikh sistem, preprint No 15/2004, POMI

[Su4] Suslina T. A., “Ob usrednenii periodicheskikh parabolicheskikh sistem”, Funkts. anal. i ego pril., 38:4 (2004), 86–90 | MR | Zbl

[Shi] Shterenberg R. G., “Primer periodicheskogo magnitnogo operatora Shrëdingera s vyrozhdennym nizhnim kraem spektra”, Algebra i analiz, 16:2 (2004), 177–185 | MR | Zbl

[Sh2] Shterenberg R. G., “O strukture nizhnego kraya spektra periodicheskogo magnitnogo operatora Shrëdingera s malym magnitnym potentsialom”, Algebra i analiz, 17:5 (2005), 232–243 | MR