Skip to main content
Log in

Hölder estimates for a natural class of equations of the type of fast diffusion

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

Hölder estimates for weak solutions of doubly nonlinear parabolic equations of the type of fast diffusion with coefficients satisfying only natural growth conditions and the monotonicity requirement are obtained. Bibliography: 17 titles.

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.

Similar content being viewed by others

References

  1. A. S. Kalashnikov, “Some problems of the qualitative theory of nonlinear parabolic equations,”Russian Math. Surveys,42, 122–169 (1987).

    Article  MathSciNet  Google Scholar 

  2. P. A. Raviart, “Sur la résolution de certaines équations parabolique non linéaires,”Funct. Anal.,5, 299–328 (1970).

    MATH  MathSciNet  Google Scholar 

  3. J.-L. Lions,Quelques Méthodes de Résolution de Problèmes aux Limits Non Linéaires, Dunod, Paris (1969).

    Google Scholar 

  4. A. V. Ivanov, “Hölder estimates for quasilinear parabolic equations with double degeneracy,”Zap. Nauchn. Semin. LOMI,171, 70–105 (1989).

    MATH  Google Scholar 

  5. A. V. Ivanov, “Some forms of the maximum principle for doubly nonlinear parabolic equations,”Probl. Math. Anal.,15, 84–108 (1995).

    MATH  Google Scholar 

  6. A. V. Ivanov, “The classesB m,l and Hölder estimates for weak solutions of quasilinear doubly degenerate parabolic equations. I,” Preprint POMI E-11-91 (1991).

  7. A. V. Ivanov, “The classesB m,l and Hölder eatimates for weak solutions of quasilinear doubly degenerate parabolic equations. II,” Preprint POMI E-12-91 (1991).

  8. A. V. Ivanov, “The classesB m,l and Hölder estimates for weak solutions of quasilinear doubly degenerate parabolic equations,”Zap. Nauchn. Semin. LOMI,197, 42–70 (1992).

    MATH  Google Scholar 

  9. A. V. Ivanov, “Hölder estimates for equations of the type of slow or normal diffusion,”Zap. Nauchn. Semin. POMI,215, 130–136 (1994).

    MATH  Google Scholar 

  10. A. V. Ivanov, “Hölder estimates for equations of the type of fast diffusion,”Algebra Analiz,6, No. 4, 101–142 (1994).

    MATH  Google Scholar 

  11. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Uraltseva,Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  12. E. di Benedetto, “On the local behavior of solutions of degenerate parabolic equations with measurable coefficients,”Ann. Sci. Norm. Sup. 13 (3), 485–535 (1986).

    Google Scholar 

  13. Y. Z. Chen and E. di Benedetto, “On the local behavior of solutions of singular parabolic equations,”Arch. Rat. Mech. Anal.,103(4), 319–346 (1988).

    Google Scholar 

  14. E. di Benedetto,Degenerate Parabolic Equations, Springer-Verlag (1993).

  15. Y. Z. Chen and E. di Benedetto, “Hölder estimates of solutions of singular parabolic equations with measurable coefficients,”Arch. Rat. Mech. Anal.,118, 257–271 (1992).

    Google Scholar 

  16. A. V. Ivanov, “Existence and uniqueness of a regular solution of the Cauchy-Dirichlet problem for doubly nonlinear parabolic equations,”Z. Anal. Anwend.,14, No. 4, 751–777 (1995).

    MATH  Google Scholar 

  17. V. Vespri, “On the local behaviour of a certain class of doubly non-linear parabolic equations,”Manuscripta Math.,75, 65–80 (1992).

    MATH  MathSciNet  Google Scholar 

Download references

Authors

Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 229, 1995, pp. 29–62.

Translated by L. Yu. Kolotilina.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ivanov, A.V. Hölder estimates for a natural class of equations of the type of fast diffusion. J Math Sci 89, 1607–1630 (1998). https://doi.org/10.1007/BF02355369

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02355369

Keywords

Navigation