Behavior Near the Boundary of Positive Solutions of Second Order Parabolic Equations

Journal of Fourier Analysis and Applications

Volumn 3, Issue SPEC. ISS., 1997, Pages

  Fabes, E B ^a   Safonov, M V ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1842729670     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02656492     Document Type: Article

References (15)

1. Aronson, D.G. (1968). Non-negative solutions of linear parabolic equations, Ann. Scuola Norm. Sup. Pisa 22, 607-694.
2. Anthanasopoulos, I., Caffarelli, L.A., and Salsa, S. (1996). Caloric functions in Lipschitz domains and regularity of solutions to phase transition problems, Ann. Math. 143, 413-434.
3. Caffarelli, L., Fabes, E.B., Mortola, S., and Salsa, S. (1981). Boundary behavior of nonnegative solutions of elliptic operators in divergence form, Indiana Univ. Math. J. 30, 621-640.
4. Dahlberg, B.E.J. (1977). Estimates of harmonic measure, Arch. Rational Mech. Anal. 65, 275-288.
5. Fabes, E.B., Garofalo, N., and Salsa, S. (1986). A backward Harnack inequality and Fatou theorem for nonnegative solutions of parabolic equations, Illinois J. Math. 30, 536-565.
6. Fabes, E.B., Safonov, M.V., and Yuan, Y. Behavior near the boundary of positive solutions of second order parabolic equations, submitted to Trans. Amer. Math. Soc.
7. Garofalo, N. (1984). Second order parabolic equations in nonvariational form: boundary Harnack principle and comparison theorems for nonnegative solutions, Ann. Mat. Pura Appl. 138, 267-296.
8. Hunt, R.A. and Wheeden, R.L. (1968). On the boundary values of harmonic functions, Trans. Amer. Math. Soc. 132, 307-322.
9. Hunt, R.A. and Wheeden, R.L. (1970). Positive harmonic functions in Lipschitz domains, Trans. Amer. Math. Soc. 147, 507-527.
10. Jerison, D. and Kenig, C.E. (1982). Boundary behavior of harmonic functions in non-tangentially accessible domains, Adv. Math. 46, 80-147.
11. Littman, W., Stampacchia, G., and Weinberger, H.F. (1963). Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa, S. III. 17, 45-79.
12. Moser, J. (1964-1967). A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math. 17 (1964), 101-134; and correction in: Comm. Pure Appl. Math. 20 (1967), 231-236.
13. Moser, J. (1964-1967). A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math. 17 (1964), 101-134; and correction in: Comm. Pure Appl. Math. 20 (1967), 231-236.
14. Moser, J. (1971). On a pointwise estimate for parabolic differential equations, Comm. Pure Appl. Math. 24, 727-740.
15. Salsa, S. (1981). Some properties of nonnegative solutions of parabolic differential operators, Ann. Mat. Pura Appl. 128, 193-206.