Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aronson, D.G., Bounds for the fundamental solution of a parabolic equation, Bulletin of the AMS 73 (1967), 890–896.
Aronson, D.G., Non-negative solutions of linear parabolic equations, Ann. Sci. Norm. Sup. Pisa, 22 (1968), 607–94.
Davies, E.B., Heat Kernels and Spectral Theory, Cambridge Tracts in Mathematics, 92, Cambridge University Press, 1989.
Fabes, E.B., Stroock, D.W., A new proof of Moser's parabolic Harnack inequality via the old ideas of Nash, Arch. Rat. Mech. Anal. 96 (1986), 327–338.
Gutierrez, C.E., Wheeden, R.L., Bounds for the fundamental solution of degenerate parabolic equations, to appear in the Communications of P.D.E.
Moser, J. A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math. 17 (1964), 101–134.
Moser, J. Correction to ‘A Harnack inequality for parabolic differential equation', Comm. Pure Appl. Math. 20 (1967), 232–236.
Nash, J., Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958), 931–954.
Saloff-Coste, Laurent, Uniformly elliptic operators on Riemannian manifolds, Journal Differential Geometry.
Saloff-Coste, Laurent, A note on Poincaré, Sobolev, and Harnack inequalities, International Mathematics Research Notices, Duke Journal, No. 2 (1992), 27–37.
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag
About this chapter
Cite this chapter
Fabes, E.B. (1993). Gaussian upper bounds on fundamental solutions of parabolic equations; the method of nash. In: Dell'Antonio, G., Mosco, U. (eds) Dirichlet Forms. Lecture Notes in Mathematics, vol 1563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074089
Download citation
DOI: https://doi.org/10.1007/BFb0074089
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57421-7
Online ISBN: 978-3-540-48151-5
eBook Packages: Springer Book Archive