On the behavior of the solutions of degenerate parabolic equations

Nagoya Mathematical Journal

Volumn 155, Issue , 1999, Pages 1-26

  Ishige, Kazuhiro ^a  

^a NAGOYA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002155550     PISSN: 00277630     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0027763000006978     Document Type: Article

References (20)

1. F. Chiarenza and R. Serapinoi, Degenerate parabolic equations and Harnack inequality, Annali di Mat. Pura Appl., 4 (1983), 139-162.
2. F. Chiarenza and R. Serapinoi, A Harnack inequality for degenerate parabolic equations, Comm. in P. D. E., 9 (1984), 719-749.
3. F. Chiarenza and R. Serapinoi, A remark on a Harnack inequality for degenerate parabolic equations, Rend. Sem. Mat. Univ. Padova, 73 (1985), 179-190.
4. S. Chanillo and R. L. Wheeden, Harnack's inequality and mean-value inequalities for solutions of degenerate elliptic equations, Comm. in P. D. E., 11 (1986), 1111-1134.
5. E. B. Fabes, N. Garofalo, and S. Salsa, A backward Harnack inequality and Fatou theorem for nonnegative solutions of parabolic equations, Illinois J. Math., 30 (1986), 536-565.
6. E. B. Fabes, C. E. Kenig, and R. P. Serapioni, The local regularity of solutions of degenerate elliptic equations, Comm. P. D. E., 7 (1982), 77-116.
7. C. E. Gutiérrez and R. L. Wheeden, Mean value and Harnack inequalities for degenerate parabolic equations, Colloquium Math., dedicated to A. Zygmund, LX/LXI (1990), 157-194.
8. C. E. Gutiérrez and R. L. Wheeden, Harnack's inequality for degenerate parabolic equations, Comm, P. D. E., 16 (1991), 745-770.
9. J. Heinonen, T. Kilpeläinen, and O. Martio, Nonlinear potential theory of degenerate elliptic equations, Clarendon Press, New York, 1993.
10. J. T. Kemper, A boundary Harnack principle for Lipschitz domain and the principle of positive singularities, Comm. Pure and Appl. Math., XXV (1972), 247-255..
11. O. A. Ladyzeskayaya, N. S. Solonikov and N. N. Ural'tseva, Linear and quasilinear equations of parabolic type, Transl. Math. Monographs, 23, Amer. Math. Soc., Providence, R. I., 1968.
12. C. B. Morrey, Multiple integrals in the calculus of variations, Springer-Verlag, Berlin-Heidelberg-New York, 1966.
13. J. Moser, A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math., 17 (1964), 101-134.
14. L. Saloff-Coste, A note on Poincaré, Sobolev, and Harnack inequality, Duke Math. J., I. M. R. N., 2 (1992), 27-38.
15. L. Saloff-Coste, Parabolic Harnack inequality for divergence form second order differential operators, Potential Analysis, 4 (1995), 429-467.
16. S. Salsa, Some properties of nonnegative solutions of parabolic differential operators, Ann. Mat. Pure Appl., 128 (1981), 193-206.
17. J. Serrin, Local behavior of solutions of quasi-linear equations, Acta Math., III (1964), 247-302.
18. G. Stampacchia, Équations elliptiques du second ordre á coefficients discontinus, Les Presses De l'Université, 1966.
19. E. M. Stein, Harmonic analysis, Princeton University Press, Princeton, 1992.
20. N. S. Trudinger, Pointwise estimates and quasilinear parabolic equations, Comm. Pure Appl. Math., 21 (1968), 205-226.