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Weighted Poincaré Inequalities for Hörmander Vector Fields and local regularity for a class of degenerate elliptic equations

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Abstract

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 

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  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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