Skip to main content
Log in

Fundamental solutions for degenerate parabolic equations

  • Published:
Acta Mathematica

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Aronson, D. G., Non-negative solutions of linear parabolic equations.Ann. Scuola Norm. Sup. Pisa, 22 (1968), 607–694.

    MATH  MathSciNet  Google Scholar 

  2. Aronson, D. G. &Besala, P., Parabolic equations with unbounded coefficients.J. Differential Equations, 3 (1967), 1–14.

    Article  MathSciNet  Google Scholar 

  3. Freidlin, M. I., On the factorization of nonnegative definite matrices.Theor. Probability Appl., 13 (1968), 354–356. [Teor. Verojatnost Primenen., 13 (1968), 375–378.]

    Article  MATH  MathSciNet  Google Scholar 

  4. Friedman, A.,Partial Differential Equations of Parabolic Type. Prentice-Hall, Englewood Cliffs, N.J., 1964.

    Google Scholar 

  5. —, Uniqueness for the Cauchy problem for degenerate parabolic equations.Pacific J. Math., 46 (1973), 131–147.

    MATH  MathSciNet  Google Scholar 

  6. Friedman, A., Non-attainability of a set by a diffusion process.Trans. Amer. Math. Soc. (1974). To appear.

  7. Friedman, A. &Pinsky, M. A., Asymptotic stability and spiraling properties of solutions of stochastic equations.Trans. Amer. Math. Soc., 186 (1973), 331–358.

    Article  MathSciNet  Google Scholar 

  8. Gikhman, I. I. &Skorokhod, A. V.,Introduction to the Theory of Random Processes. W.B. Saunders Company, London, 1965.

    Google Scholar 

  9. Gikhman, I. I. &Skorokhod, A. V.,Stochastic Differential Equations. Naukova Dumka, Kiev, 1968.

    Google Scholar 

  10. Ito, S., The fundamental solution of the parabolic equation in a differentiable manifold.Osaka J. Math., 5 (1953), 75–92.

    MATH  Google Scholar 

  11. —, Fundamental solutions of parabolic differential equations and boundary value problems.Japan J. Math., 27 (1957), 55–102.

    Google Scholar 

  12. McKean, H. P., Jr.,Stochastic Integrals. Academic Press, New York, 1969.

    Google Scholar 

  13. Phillips, R. S. &Sarason, L., Elliptic-parabolic equations of the second order.J. Math. Mech. 17 (1967/8), 891–917.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This work was partially supported by National Science Foundation Grant GP-35347X.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Friedman, A. Fundamental solutions for degenerate parabolic equations. Acta Math. 133, 171–217 (1974). https://doi.org/10.1007/BF02392145

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02392145

Keywords

Navigation