Geodesic
Estimates of the Nash–Aronson type for the diffusion equation with non-symmetric matrix and
Sbornik. Mathematics, Tome 197 (2006) no. 12, pp. 1775-1804 Cet article a éte moissonné depuis la source Math-Net.Ru

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     url = {http://geodesic.mathdoc.fr/item/SM_2006_197_12_a3/}
}
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V. V. Zhikov. Estimates of the Nash–Aronson type for the diffusion equation with non-symmetric matrix and. Sbornik. Mathematics, Tome 197 (2006) no. 12, pp. 1775-1804. http://geodesic.mathdoc.fr/item/SM_2006_197_12_a3/

[1] D. G. Aronson, “Bounds for the fundamental solutions of a parabolic equation”, Bull. Amer. Math. Soc., 73 (1967), 890–896 | DOI | MR | Zbl

[2] D. G. Aronson, “Non-negative solutions of linear parabolic equations”, Ann. Scuola Norm. Sup. Pisa. Cl. Sci. (4), 22 (1968), 607–694 ; Addendum, 25 (1971), 221–228 | MR | Zbl | MR | Zbl

[3] V. V. Zhikov, S. M. Kozlov, O. A. Oleinik, Usrednenie differentsialnykh operatorov, Nauka, M., 1993 | MR | Zbl

[4] V. V. Zhikov, “Zamechaniya o edinstvennosti resheniya zadachi Dirikhle dlya ellipticheskogo uravneniya vtorogo poryadka s mladshimi chlenami”, Funkts. analiz i ego pril., 38:3 (2004), 15–28 | MR | Zbl

[5] F. O. Porper, S. D. Eidelman, “Dvustoronnie otsenki dlya fundamentalnykh reshenii parabolicheskikh uravnenii vtorogo poryadka i nekotorye ikh prilozheniya”, UMN, 39:3 (1984), 107–156 | MR | Zbl

[6] A. K. Guschin, “O ravnomernoi stabilizatsii reshenii vtoroi smeshannoi zadachi dlya parabolicheskogo uravneniya”, Matem. sb., 119(161):4(12) (1982), 451–508 | MR | Zbl

[7] V. V. Zhikov, “Asimptoticheskie zadachi, svyazannye s uravneniem teploprovodnosti v perforirovannykh oblastyakh”, Matem. sb., 181:10 (1990), 1283–1305 | MR | Zbl

[8] A. Grigor'yan, “Gaussian upper bounds for the heat kernel on arbitrary manifolds”, J. Differential Geom., 45:1 (1997), 33–52 | MR | Zbl

[9] E. B. Davies, Heat kernels and spectral theory, Cambridge Univ. Press, Cambridge, 1989 | MR | Zbl

[10] K. Oelschläger, “Homogenization of a diffusion process in a divergence free random field”, Ann. Probab., 16 (1988), 1084–1126 | DOI | MR | Zbl

[11] A. Fannjiang, G. Papanicolaou, “Diffusion in turbulence”, Probab. Theory and Related Fields, 105 (1996), 279–334 | DOI | MR | Zbl

[12] A. Fannjiang, T. Komorowski, “An invariance principle for diffusion in turbulence”, Ann. Probab., 27 (1999), 751–781 | DOI | MR | Zbl

[13] A. Fannjiang, T. Komorowski, “Turbulent diffusion in Markovian flows”, Ann. Appl. Probab., 9 (1999), 591–610 | DOI | MR | Zbl

[14] A. Fannjiang, T. Komorowski, “A martingale approach to homogenization of unbounded random flows”, Ann. Probab., 25 (1997), 1872–1894 | DOI | MR | Zbl

[15] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967 | MR | Zbl

[16] B. M. Levitan, V. V. Zhikov, Pochti periodicheskie funktsii i differentsialnye uravneniya, Izd-vo MGU, M., 1978 | MR | Zbl

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

[18] N. Danford, Dzh. Shvarts, Lineinye operatory. Obschaya teoriya, Mir, M., 1962 | MR | MR | Zbl

[19] V. V. Zhikov, “Diffuziya v neszhimaemom sluchainom potoke”, Funkts. analiz i ego pril., 31:3 (1997), 10–22 | MR | Zbl