Skip to main content

New estimates of the fundamental solution and Wiener’s criterion for parabolic equations with variable coefficients

Part of the Lecture Notes in Mathematics book series (LNM,volume 1340)

Keywords

  • Parabolic Equation
  • Dirichlet Problem
  • Fundamental Solution
  • Variable Coefficient
  • Explicit Knowledge

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Berger, P. Gauduchon et E. Mazet, Le Spectre d’une Variété Riemanniene, Lecture Notes in Math., Springer-Verlag 194, 1971.

    Google Scholar 

  2. L.C. Evans and R.F. Gariepy, Wiener’s Criterion for the Heat Equation, Arch. Rat. Mech. Anal. 78 (1982), 293–314.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. E.B. Fabes and N. Garofalo, Mean Value Properties of Solutions to Parabolic Equations with Variable Coefficients, Journal of Math. Analysis and Applications, J. of Math. Analysis and Appl. 121 (1987), 305–316.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. H. Federer, Geometric Measure Theory, Die Grundlehren der mathematischen Wissenschaften, Springer-Verlag 1969.

    Google Scholar 

  5. W. Fulks, A Mean Value Theorem for the Heat Equation, Proc. Amer. Math. Soc. 17 (1966), 6–11.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. N. Garofalo and E. Lanconelli, New Estimates of the Fundamental Solution and Wiener’s Criterion for Parabolic Equations with Variable Coefficients, preprint.

    Google Scholar 

  7. Y. Kannai, Off Diagonal Short Time Asymptotics for Fundamental Solutions of Diffusion Equations, Comm. in P.D.E. 2 (8) (1977), 781–830.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. E. Lanconelli, Sul problema di Dirichlet per l’equazione del calore, Ann. di Mat. Pura e Appl. 97 (1973), 83–114.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. E. Lanconelli, Sul problema di Dirichlet per equazioni paraboliche del secondo ordine a coefficienti discontinui, Ann. di Mat. Pura e Appl. 106 (1975), 11–38.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. W. Littman, G. Stampacchia and H.F. Weinberger, Regular Points for Elliptic Equations with Discontinuous Coefficients, Ann. Scuola Norm. Sup. Pisa 17 (1963).

    Google Scholar 

  11. I. Petrovskii, Zur ersten Randwertaufgabe der Wärmeleitungsgleichung, Compositio Mathematica 1 (1935), 383–419.

    MathSciNet  MATH  Google Scholar 

  12. B. Pini, Sulle equazioni a derivate parziali, lineari del secondo ordine in due variabili, di tipo parabolico, Ann. di Mat. Pura e Appl. 32 (1951), 179–204.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. B. Pini, Maggioranti e minoranti delle soluzioni delle equazioni paraboliche, Ann. di Mat. Pura e Appl. 37 (1954), 249–264.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. B. Pini, Sulla soluzione generalizzata di Wiener per il primo problema di valori al contorno nel caso parabolico, Rend. Sem. Mat. Univ. Padova 23 (1954), 422–434.

    MathSciNet  MATH  Google Scholar 

  15. N.A. Watson, A Theory of Temperatures in Several Variables, Proc. London Math. Soc. 26 (3) (1973), 385–417.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. N. Wiener, The Dirichlet Problem, J. Math. and Phys. 3 (1924), 127–146.

    CrossRef  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Additional information

Dedicated to Hans Lewy

Rights and permissions

Reprints and Permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Garofalo, N. (1988). New estimates of the fundamental solution and Wiener’s criterion for parabolic equations with variable coefficients. In: Hildebrandt, S., Kinderlehrer, D., Miranda, M. (eds) Calculus of Variations and Partial Differential Equations. Lecture Notes in Mathematics, vol 1340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082886

Download citation

  • DOI: https://doi.org/10.1007/BFb0082886

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50119-0

  • Online ISBN: 978-3-540-45932-3

  • eBook Packages: Springer Book Archive