Voir la notice de l'article provenant de la source Math-Net.Ru
@article{AA_2012_24_6_a5, author = {M. A. Pakhnin and T. A. Suslina}, title = {Operator error estimates for homogenization of the elliptic {Dirichlet} problem in a~bounded domain}, journal = {Algebra i analiz}, pages = {139--177}, publisher = {mathdoc}, volume = {24}, number = {6}, year = {2012}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/AA_2012_24_6_a5/} }
TY - JOUR AU - M. A. Pakhnin AU - T. A. Suslina TI - Operator error estimates for homogenization of the elliptic Dirichlet problem in a~bounded domain JO - Algebra i analiz PY - 2012 SP - 139 EP - 177 VL - 24 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/AA_2012_24_6_a5/ LA - ru ID - AA_2012_24_6_a5 ER -
M. A. Pakhnin; T. A. Suslina. Operator error estimates for homogenization of the elliptic Dirichlet problem in a~bounded domain. Algebra i analiz, Tome 24 (2012) no. 6, pp. 139-177. http://geodesic.mathdoc.fr/item/AA_2012_24_6_a5/
[1] Bakhvalov N. S., Panasenko G. P., Osrednenie protsessov v periodicheskikh sredakh, Nauka, M., 1984 | MR | Zbl
[2] Bensoussan A., Lions J.-L., Papanicolaou G., Asymptotic analysis for periodic structures, Stud. Math. Appl., 5, North-Holland Publ. Co., Amsterdam–New York, 1978 | MR | Zbl
[3] 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
[4] 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
[5] Birman M. Sh., Suslina T. A., “Porogovye approksimatsii rezolventy faktorizovannogo samosopryazhennogo semeistva s uchetom korrektora”, Algebra i analiz, 17:5 (2005), 69–90 | MR | Zbl
[6] Birman M. Sh., Suslina T. A., “Usrednenie periodicheskikh ellipticheskikh differentsialnykh operatorov s uchetom korrektora”, Algebra i analiz, 17:6 (2005), 1–104 | MR | Zbl
[7] Birman M. Sh., Suslina T. A., “Usrednenie periodicheskikh differentsialnykh operatorov s uchetom korrektora. Priblizhenie reshenii v klasse Soboleva $H^1 (\mathbb R^d)$”, Algebra i analiz, 18:6 (2006), 1–130 | MR | Zbl
[8] Griso G., “Error estimate and unfolding for periodic homogenization”, Asymptot. Anal., 40 (2004), 269–286 | MR | Zbl
[9] Griso G., “Interior error estimate for periodic homogenization”, Anal. Appl. (Singap.), 4:1 (2006), 61–79 | DOI | MR | Zbl
[10] Zhikov V. V., “Ob operatornykh otsenkakh v teorii usredneniya”, Dokl. RAN, 403:3 (2005), 305–308 | MR | Zbl
[11] Zhikov V. V., “O nekotorykh otsenkakh iz teorii usredneniya”, Dokl. RAN, 406:5 (2006), 597–601 | MR | Zbl
[12] Zhikov V. V., Kozlov S. M., Oleinik O. A., Usrednenie differentsialnykh operatorov, Nauka, M., 1993 | MR
[13] Zhikov V. V., Pastukhova S. E., “On operator estimates for some problems in homogenization theory”, Russ. J. Math. Phys., 12:4 (2005), 515–524 | MR | Zbl
[14] McLean W., Strongly elliptic systems and boundary integral equations, Cambridge Univ. Press, Cambridge, 2000 | MR | Zbl
[15] Pastukhova S. E., “O nekotorykh otsenkakh iz usredneniya zadach teorii uprugosti”, Dokl. RAN, 406:5 (2006), 604–608 | MR | Zbl
[16] Pakhnin M. A., Suslina T. A., “Usrednenie ellipticheskoi zadachi Dirikhle: otsenki pogreshnosti v $(L_2\to H^1)$-norme”, Funkts. anal. i ego pril., 46:2 (2012), 92–96 | DOI | MR
[17] Suslina T. A., “Operatornye otsenki pogreshnosti v $L_2$ pri usrednenii ellipticheskoi zadachi Dirikhle”, Funkts. anal. i ego pril., 46:3 (2012), 91–96 | DOI
[18] Suslina T. A., “Homogenization of the elliptic Dirichlet problem: operator error estimates in $L_2$”, Mathematika (to appear); Preprint, 2012, arXiv: 1201.2286