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On a Harnack inequality for nonlinear parabolic equations. (English) Zbl 0162.42102

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[1] Friedman, A., Partial differential equations of parabolic type, Prentice-Hall, En- glewood Cliffs, N. J., 1964. · Zbl 0144.34903
[2] Moser, J, A new proof of de Giorgi’s theorem concerning the regularity pro- blem for elliptic differential equations, Comm. Pure Appl. Math. 13 (1960), 457-468. · Zbl 0111.09301 · doi:10.1002/cpa.3160130308
[3] , On Harnack’s theorem for elliptic differential equations, Ibid. 14 (1961), 577-591. · Zbl 0111.09302 · doi:10.1002/cpa.3160140329
[4] , On the regularity problem for elliptic and parabolic differential equa- tions, Partial Differential Equations and Continuum Mechanics, The University of Wisconsin Press (1961), 159-169. · Zbl 0111.09401
[5] , A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math. 17 (1964), 101-134. · Zbl 0149.06902 · doi:10.1002/cpa.3160170106
[6] ? Correction to ”A Harnack inequality for parabolic differential equa- tions”, Comm. Pure Appl. Math. 20 (1967), 231-236. · Zbl 0149.07001 · doi:10.1002/cpa.3160200107
[7] Nash, J., Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958), 931-954. · Zbl 0096.06902 · doi:10.2307/2372841
[8] Nirenberg, L, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, 13 (1959), 1-48 · Zbl 0088.07601 · numdam:ASNSP_1959_3_13_2_115_0 · eudml:83226
[9] KpywKOB, O.H., Anpnopn on;eEKH sp^ oSotmeHHEcx pemennii ejznirraHecKHx H napaGojra- HGCKHX ypaBnennt Bioporo nopa^Ka, JIoio. AK&U. HayK COOP, 150 (1963), 748-751.
[10] -, 0 HeKOTOpHx CBoncTBax pemeHnn ejrjranTHHecKnx ypaBHenennn, JFoM. Anas. HayK COOP, 150 (1963), 470-473.
[11] __ , AnpnopHHe on;enKn H neKOTOpne csoftcTEa pemennn eMHUTnHCsnx n na- pa6ojraHecKHx ypadneHHM, Max. 06. 65 (1964), 522-570.
[12] John, F. and L. Nirenberg, On functions of bounded mean oscillations, Comm. Pure Appl. Math. 14 (1964), 415-426. · Zbl 0102.04302 · doi:10.1002/cpa.3160140317
[13] Serrin, J., Local behavior of solutions of quasi-linear equations, Acta Math. Ill (1964), 247-302. · Zbl 0128.09101 · doi:10.1007/BF02391014
[14] Kurihara, M., On a Harnack inequality for parabolic equations I, Funkcial. Ekvac. 17, No. 3 (1965), 3-57. (Japanese)
[15] - , On a Harnack inequality for parabolic equations II, Ibid. 18, Nos. 1/2 (1965), 3-32. (Japanese) Note added in proof (August 25, 1967) : Recently we knew that D.G. Aronson and J. Serrin and following them A. B. HeaHOB had obtained the same results as ours. Aronson, D.G. and J. Serrin, A Harnack inequality for nonlinear parabolic equations, Notices Amer. Math. Soc. 13, No. 3 (1966), 381. HB3HOB, A.B., HepaBCHCTBO rapnaKa ,zyra o6o6meHHbix pemenHH KdasiiJiPiHenHbix napa6ojiHHecKHx ypaBHCHHH BTOporo nopanKa, /JOKJI. AKa#. HayK CCCP, 173 (1967), 752-754. Aronson, D.G. and J. Serrin, Local behavior of solutions of quasi- linear parabolic equations, Arch. Rational Mech. Anal. Vol. 25, No. 2 (1967), 81-122.
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