Skip to main content
SpringerLink
Log in

A Harnack inequality for the equation ∇(a∇u)+b∇u=0, when |b|∈Kn+1

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

By proving a lower and an upper bound of the fundamental solutions of certain parabolic equations, we establish a Harnack inequality for some parabolic and elliptic equations which include: ∇(a∇u)+b∇u=0, |b|∈K n+1.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D.G. Aronson,Non-negative solutions of linear parabolic equations, Annali della Scuola Norm. Sup. PisaXXII (1968), 607–694

    MathSciNet  Google Scholar 

  2. M. Aizenman and B. Simon,Brownian motion and Harnack's inequality for Schrödinger operators, Comm. Pure Appl. Math35 (1982), 209–271

    MATH  MathSciNet  Google Scholar 

  3. F. Chiarenza, E. Fabes and N. Garofalo,Harnack's inequality for Schrödinger operators and the continuity of solutions, Proc. Amer. Math. Soc.307 (1986), 415–425

    Article  MathSciNet  Google Scholar 

  4. M. Cranston and Z. Zhao, Conditional transformation of drift formula and potential theory for\(\frac{1}{2}\Delta + b( \cdot )\nabla \), Comm. Math. Phys.112 (1987), 613–625

    Article  MATH  MathSciNet  Google Scholar 

  5. M. Cranston, E. Fabes, Z. Zhao,Conditional gauge and potential theory for the Schrödinger operator, Trans. Amer. Math. Soc.307 (1988), 171–194

    Article  MATH  MathSciNet  Google Scholar 

  6. E.B. Fabes and D.W. Stroock,A new proof of Moser's parabolic Harnack inequality using the old idea of Nash, Archive of RMA.96 (1986), 327–338.

    MATH  MathSciNet  Google Scholar 

  7. K. Kurata,Continuity and Harnack's inequality for solutions of elliptic equations of second order, Indiana Univ. Math. J.43 (1994), 411–441.

    Article  MATH  MathSciNet  Google Scholar 

  8. O.A. Ladyzhenskaya and V. A. Solonnikov and N. N. Uralceva,Linear and quasilinear equations of parabolic type, Providence, AMS

  9. K. Sturm,Harnack's inequality for parabolic operators with singular low order terms, Math. Z.216, 593–612

  10. F. Treves,Basic Linear Partial Differential Equations, Academic Press 1975

  11. Qi Zhang,On a parabolic equation with a singular lower order term., Transactions of AMS, to appear

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Purdue University, 47907, West Lafayette, IN, USA

    Qi Zhang

Authors
  1. Qi Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, Q. A Harnack inequality for the equation ∇(a∇u)+b∇u=0, when |b|∈Kn+1 . Manuscripta Math 89, 61–77 (1996). https://doi.org/10.1007/BF02567505

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02567505

Keywords

Search

Navigation