Singular solutions of semilinear elliptic and parabolic equations

Mathematische Annalen

Volumn 310, Issue 4, 1998, Pages 777-794

  Zhang, Qi S ^a   Zhao, Z ^a  

^a UNIVERSITY OF MISSOURI   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032397079     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002080050170     Document Type: Article

References (31)

1. D. Aronson, Non-negative solutions of linear parabolic equations, Annali della Scuola Norm. Sup. Pisa 22 (1968), 607-694.
2. I. Athanasopoulos, L. Caffarelli, S. Salsa, Caloric functions in Lipschitz doamins and the regularity of solutions to phase transition problems, Annals Math. 143 (1996), 413-434.
3. P. Aviles, Local behavior of solutions of some elliptic equations, Comm. Math. Phy. 108 (1987), 177-192.
4. M. Aizenman, B. Simon, Brownian motion and Harnack's inequality for Schrödinger operators, Comm. Pure Appl. Math 35 (1982), 209-271.
5. C. Bandle, M. Marcus, The positive radial solutions of a class of semilinear elliptic equations, J. reine angew. Math 401 (1989), 25-59.
6. H. Brezis, L. Oswald, Singular solutions of some semilinear elliptic equations, Arch. Rat. Mech. Anal. 99 (1987), 249-259.
7. M. Cranston, E. Fabes, Z. Zhao, Conditional gauge and potential theory for the Schrödinger operator, Trans. Amer. Math. Soc. 307 (1988), 171-194.
8. L. Caffarelli, B. Gidas, J. Spruck, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. PAM. 42 (1989), 271-297.
9. K. L. Chung, Z. Zhao, From Brownian motion to Schödinger's equation, Springer, Berlin (1995)
10. 1+α, J. Fac. Sci. Univ. Tokyo, Sect 113 (1966), 109-124.
11. E. Fabes, M. Safonov, pre-print 1996
12. B. Gidas, J. Spruck, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. PAM. 34 (1981), 525-598.
13. M. Guedda, L. Veron, local properties of positive solutions of quasilinear elliptic equations, J. Diff. Eq. 76 (1988), 159-189.
14. D. Jerison, C. Kenig, Boundary Behavior of Harmonic Functions in Non-tangentially Accessible Domains, Advances in Math. 46 (1982), 80-147.
15. C. Kenig, Harmonic analysis techniques dor second order elliptic boundary value problems, CBMS Series in Mathematics, No. 83, AMS (1984)
16. C. Kenig, W. M. Ni, An exterior Dirichlet problem with applications to some equations arising in geometry, Amer. J. Math. 106 (1984), 689-702.
17. N. J. Kalton, I. E. Verbitsky, Nonlinear equations and weighted norm inequality, pre-print
18. P. L. Lions, Isolated singularities in semilinear problems, J. Diff. Eq. 38 (1980), 441-450.
19. Yi Li, J. Santanilla, Existence and nonexistence of positive singular solutions for semi-linear elliptic problems with applications in astrophysics, Diff. and Int. Eq. 8 (1995), 1369-1383.
20. W. M. Ni, Uniqueness, nonuniqueness and related questions of nonlinear elliptic and parabolic equations, Proc. Symposia Pure Math. 39 (1986), 379-399.
21. W. M. Ni, P. Sacks, Singular behavior in nonlinear parabolic equations, Tran. Amer. Math. Soc. 287 (1985), 657-671.
22. W. M. Ni, J. Serrin, Nonexistence theorems for singular solutions of quasilinear partial differential equations, Comm. PAM. 39 (1986), 379-399.
23. T. Senba, Y. Ebihara, Y. Furusho, Dirichlet problem for a semilinear elliptic equation with singular coefficient , Non. Anal. TMA. 15 (1990), 299-306.
24. J. Serrin, Isolated singularities of solutions of quasilinear equations, Acta Math. 113 (1965), 219-240.
25. J. Serrin, Local behavior of quasilinear equations, Act Math. 113 (1965), 247-301.
26. B. Simon, Schrödinger semigroup, Bull. AMS. 7 (1982), 447-526.
27. p, Indiana Univ. Math. J 29 (1980), 79-102.
28. Qi Zhang, On a parabolic equation with a singular lower order term, Transactions of AMS 348 (July, 1996), 2811-2844.
29. Qi Zhang, Global existence and local continuity of solutions for semilinear parabolic equations, Comm. PDE 22 (1997), 1529-1557.
30. Z. Zhao, On the existence of positive solutions of nonlinear elliptic equations- A probabilistic potential theory approach, Duke Math J. 69 (1993), 247-258.
31. Z. Zhao, Subcriticality, positivity, and gaugeability of the Schrödinger operator, Bull. AMS 23 (1990), 513-517.