Explicit estimates on the fundamental solution of higher-order parabolic equations with measurable coefficients

Journal of Differential Equations

Volumn 174, Issue 2, 2001, Pages 442-463

  Barbatis, G ^a  

^a UNIVERSITY OF CRETE   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035839352     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2000.3940     Document Type: Article

References (19)

1. S. Agmon, "Lectures on Exponential Decay of Solutions of Second-order Elliptic Equations," Mathematical Notes, Princeton University Press, Princeton, NJ, 1982.
2. P. Abate and G. Patrizo, "Finsler metrics - A global approach," Lecture Notes in Mathematics, Vol. 1591, Springer-Verlag, Berlin/New York, 1994.
3. P. Auscher and M. Qafsaoui, Equivalence between regularity theorems and heat kernel estimates for higher order elliptic operators and systems under divergence form, J. Funct. Anal. 177 (2000), 310-364.
4. G. Barbatis and E. B. Davies, Sharp bounds on heat kernels of higher order uniformly elliptic operators, J. Operator Theory 36 (1996), 179-198.
5. G. Barbatis, Sharp heat kernel bounds and finsler-type metrics, Quart. J. Math. Oxford 49 (1998), 261-277.
6. G. Barbatis, Spectral theory of singular elliptic operators with measurable coefficients, J. Funct. Anal. 155 (1998), 125-152.
7. G. Barbatis, On the approximation of finsler metrics on euclidean domains, Proc. Edinburgh Math. Soc. 42 (1999), 589-609.
8. E. B. Davies, Uniformly elliptic operators with measurable coefficients, J. Funct. Anal. 132 (1995), 141-169.
9. P spectral theory of higher-order elliptic differential operators, Bull. London Math. Soc. 29 (1997), 513-546.
10. P regularity of self-adjoint elliptic operators, J. Differential Equations 135 (1997), 83-102.
11. A. F. M. Elst and D. W. Robinson, High order divergence-form elliptic operators on lie groups, Bull. Austral. Math. Soc. 55 (1997), 335-348.
12. M. A. Evgrafov and M. M. Postnikov, Asymptotic behavior of green's functions for parabolic and elliptic equations with constant coefficients, Math. USSR Sb. 11 (1970), 1-24.
13. M. A. Evgrafov and M. M. Postnikov, More on the asymptotic behavior of the green's function of parabolic equations with constant coefficients, Math. USSR Sb. 92(134) (1973), 171-194.
14. P spectrum of elliptic operators, J. Math. Mech. Appl. 108 (1985), 223-229.
15. P and spectral theory for a class of global elliptic operators, J. Operator Theory 19 (1988), 243-274.
16. P-theory of elliptic differential operators on manifolds of bounded geometry, Acta Appl. Math. 23 (1991), 223-260.
17. D. W. Robinson, "Elliptic Operators and Lie Groups," Oxford Univ. Press, London/New York, 1991.
18. H. Rund, "The Differential Geometry of Finsler Spaces," Springer-Verlag, 1959.
19. K. Tintarev, Short time asymptotics for fundamental solutions of higher order parabolic equations, Comm. Partial Differential Equations 7 (1982), 371-391.