Potential Analysis

, Volume 4, Issue 4, pp 361–375

Weighted Poincaré inequalities for Hörmander vector fields and local regularity for a class of degenerate elliptic equations

  • B. Franchi
  • G. Lu
  • R. L. Wheeden

DOI: 10.1007/BF01053453

Cite this article as:
Franchi, B., Lu, G. & Wheeden, R.L. Potential Anal (1995) 4: 361. doi:10.1007/BF01053453


In this note we state weighted Poincaré inequalities associated with a family of vector fields satisfying Hörmander rank condition. Then, applications are given to relative isoperimetric inequalities and to local regularity (Harnack's inequality) for a class of degenerate elliptic equations with measurable coefficients.

Key words

Hörmander vector fields Poincaré inequality relative isoperimetric inequality Harnack's inequality 

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • B. Franchi
    • 1
  • G. Lu
    • 2
  • R. L. Wheeden
    • 3
  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaItaly
  2. 2.Department of MathematicsWright State UniversityDaytonUSA
  3. 3.Department of MathematicsRutgers UniversityNew BrunswickUSA

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