The Harnack inequality and related properties for solutions to elliptic and parabolic equations with divergence-free lower-order coefficients
Algebra i analiz, Tome 23 (2011) no. 1, pp. 136-168.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{AA_2011_23_1_a4,
     author = {A. I. Nazarov and N. N. Uraltseva},
     title = {The {Harnack} inequality and related properties for solutions to elliptic and parabolic equations with divergence-free lower-order coefficients},
     journal = {Algebra i analiz},
     pages = {136--168},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2011_23_1_a4/}
}
TY  - JOUR
AU  - A. I. Nazarov
AU  - N. N. Uraltseva
TI  - The Harnack inequality and related properties for solutions to elliptic and parabolic equations with divergence-free lower-order coefficients
JO  - Algebra i analiz
PY  - 2011
SP  - 136
EP  - 168
VL  - 23
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2011_23_1_a4/
LA  - ru
ID  - AA_2011_23_1_a4
ER  - 
%0 Journal Article
%A A. I. Nazarov
%A N. N. Uraltseva
%T The Harnack inequality and related properties for solutions to elliptic and parabolic equations with divergence-free lower-order coefficients
%J Algebra i analiz
%D 2011
%P 136-168
%V 23
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2011_23_1_a4/
%G ru
%F AA_2011_23_1_a4
A. I. Nazarov; N. N. Uraltseva. The Harnack inequality and related properties for solutions to elliptic and parabolic equations with divergence-free lower-order coefficients. Algebra i analiz, Tome 23 (2011) no. 1, pp. 136-168. http://geodesic.mathdoc.fr/item/AA_2011_23_1_a4/

[1] De Giorgi E.,, “Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari”, Mem. Acad. Sci. Torino. Cl. Sci. Fis. Mat. Nat. (3), 3 (1957), 25–43 | MR | Zbl

[2] Morrey C. B. (jr.), “Second order elliptic equations in several variables and Hölder continuity”, Math. Z., 72 (1959–1960), 146–164 | DOI | MR | Zbl

[3] Nash J., “Parabolic equations”, Proc. Nat. Acad. Sci. USA, 43 (1957), 754–758 | DOI | MR | Zbl

[4] Ladyzhenskaya O. A., Uraltseva N. N., “Kraevaya zadacha dlya lineinykh i kvazilineinykh parabolicheskikh uravnenii”, Dokl. AN SSSR, 139:3 (1961), 544–547 | Zbl

[5] Moser J., “On Harnack's theorem for elliptic differential equations”, Comm. Pure Appl. Math., 14 (1961), 577–591 | DOI | MR | Zbl

[6] Moser J., “A Harnack inequality for parabolic differential equations”, Comm. Pure Appl. Math., 17 (1964), 101–134 ; “Correction”, Comm. Pure Appl. Math., 20 (1967), 231–236 | DOI | MR | Zbl | DOI | MR | Zbl

[7] Nazarov A. I., Ural'tseva N. N., Qualitative properties of solutions to elliptic and parabolic equations with unbounded lower-order coefficients, SPbMS El. Prepr. Archive, No 2009-05, 6 pp.

[8] Zhang Qi. S., “A strong regularity result for parabolic equations”, Comm. Math. Phys., 244:2 (2004), 245–260 | DOI | MR | Zbl

[9] Koch G., Nadirashvili N., Seregin G., Šverák V., “Liouville theorems for the Navier–Stokes equations and applications”, Acta Math., 203:1 (2009), 83–105 | DOI | MR | Zbl

[10] Chen C.-C., Strain R. M., Tsai T.-P., Yau H.-T., “Lower bound on the blow-up rate of the axisymmetric Navier–Stokes equations, I”, Int. Math. Res. Not., 2008:9 (2008), Art. ID rnn016, 31 pp. ; “II”, Comm. Partial Differential Equations, 34:1–3 (2009), 203–232 | MR | DOI | MR | Zbl

[11] Seregin G., Silvestre L., Šverák V., Zlatos A., On divergence-free drifts, arXiv: 1010.6025v1

[12] Trudinger N. S., “Linear elliptic operators with measurable coefficients”, Ann. Scuola Norm. Sup. Pisa (3), 27 (1973), 265–308 | MR | Zbl

[13] Lieberman G. M., Second order parabolic differential equations, World Sci. Publ. Co. Inc., River Edge, NJ, 1996 | MR | Zbl

[14] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, izd. 2, Nauka, M., 1973 | MR

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

[16] Lib E., Loss M., Analiz, Nauch. kn., Novosibirsk, 1998

[17] Safonov M. V., “Teoremy o srednem i neravenstva Garnaka dlya parabolicheskikh uravnenii vtorogo poryadka”, Nelineinye zadachi matematicheskoi fiziki i smezhnye voprosy, v. II, Mezhdunar. mat. ser., 2, Tamara Rozhkovskaya, Novosibirsk, 2002, 299–320 | MR

[18] Maz'ya V. G., Verbitsky I. E., “Form boundedness of the general second order differential operator”, Comm. Pure Appl. Math., 59 (2006), 1286–1329 | DOI | MR | Zbl

[19] Troianiello G. M., Elliptic differential equations and obstacle problems, Plenum Press, New York, 1987 | MR | Zbl

[20] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, izd. 2, Nauka, M., 1996 | MR

[21] Safonov M. V., “Non-divergence elliptic equations of second order with unbounded drift”, Amer. Math. Soc. Transl. Ser. 2, 229, Amer. Math. Soc., Providence, RI, 2010, 211–232 | MR | Zbl