Hostname: page-component-848d4c4894-xfwgj Total loading time: 0 Render date: 2024-06-27T13:09:31.886Z Has data issue: false hasContentIssue false
  • English
  • Français

On the approximation of Finsler metrics on Euclidean domains

Published online by Cambridge University Press:  20 January 2009

G. Barbatis
G. Barbatis
Affiliation:
Department of Mathematics, King's College, Strand London WC2R 2LS, England
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove that Finsler metrics on Euclidean domains can be approximated in a certain sense by so-called Finsler-type metrics. As an application we improve upon previous estimates on the fundamental solution of higher order parabolic equations.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 3 , October 1999 , pp. 589 - 609
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

REFERENCES

1.Abate, M. and Patrizo, G., Finsler metrics – a global approach (Lecture Notes in Mathematics, 1591, Springer, 1994).CrossRefGoogle Scholar
2.Agmon, S., Lectures on exponential decay of solutions of second-orderelliptic equations (Mathematical Notes, Princeton University Press, 1982).Google Scholar
3.Auscher, P., Coulhon, T. and Tchamitchian, P., Absence de principe du maximum pour certaines équations paraboliques complexes, Colloq. Math., to appear.Google Scholar
4.Barbatis, G. and Davies, E. B., Sharp bounds on heat kernels of higher-order uniformly elliptic operators, J Operator Theory 36 (1996), 179–198.Google Scholar
5.Barbatis, G., Sharp heat kernel bounds and Finsler-type metrics, Quart. J. Math. Oxford Ser. (2) 49 (1998), 261–277.CrossRefGoogle Scholar
6.Bejancu, A., Finsler geometry and applications (Ellis Horwood, 1990).Google Scholar
7.Boothby, W. M., An introduction to differentiable manifolds and Riemannian geometry (Academic Press, 1986).Google Scholar
8.Busemann, H., Metric methods in Finsler spaces and in the foundations of geometry (Princeton University Press, 1942).Google Scholar
9.Davies, E. B., Explicit constants for Gaussian upper bounds on heat kernels, Amer. J. Math. 109 (1987), 319–334.Google Scholar
10.Davies, E. B., Uniformly elliptic operators with measurable coefficients, J. Funct. Anal. 132 (1995), 141–169.CrossRefGoogle Scholar
11.Davies, E. B., L p spectral theory of higher-order elliptic differential operators, Bull. London Math. Soc. 29 (1997), 513–546.CrossRefGoogle Scholar
12.Edmunds, D. E. and Evans, W. D., Spectral theory and differential operators (Oxford University Press, 1987).Google Scholar
13.Evgrafov, M. A. and Postnikov, M. M., Asymptotic behavior of Green's functions for parabolic and elliptic equations with constant coefficients, Math. USSR-Sb. 11 (1970), 1–24.Google Scholar
14.Evgrafov, M. A. and Postnikov, M. M., More on the asymptotic behavior of the Green's functions of parabolic equations with constant coefficients, (Russian) Mat. Sb. 92 (134) (1973), 171–194.Google Scholar
15.Owen, M., A Riemannian off-diagonal heat kernel bound for uniformly elliptic operators, preprint 1997.Google Scholar
16.Robinson, D. W., Elliptic operators and Lie groups (Oxford University Press, London, New York, 1991).Google Scholar
17.Rund, H., The differential geometry of Finsler spaces (Springer-Verlag, 1959).CrossRefGoogle Scholar
18.Tintarev, K., Short time asymptotics for fundamental solutions of higher order parabolic equations, Comm. Partial Differential Equations 7 (1982), 371–391.Google Scholar