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.
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The first author thanks the Institute for Advaced Study in Princeton for its hospitality during the preparation of the manuscript.
The first author was partially supported by MURST, Italy (40% and 60%) and GNAFA of CNR, Italy.
The second and third authors were partially supported by NSF Grants DMS93-15963 and 93-02991.
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Franchi, B., Lu, G. & Wheeden, R.L. Weighted Poincaré inequalities for Hörmander vector fields and local regularity for a class of degenerate elliptic equations. Potential Anal 4, 361–375 (1995). https://doi.org/10.1007/BF01053453
- Hörmander vector fields
- Poincaré inequality
- relative isoperimetric inequality
- Harnack's inequality