B. Franchi et al., WEIGHTED POINCARE INEQUALITIES FOR HORMANDER VECTOR-FIELDS AND LOCAL REGULARITY FOR A CLASS OF DEGENERATE ELLIPTIC-EQUATIONS, Potential analysis, 4(4), 1995, pp. 361-375
In this note we state weighted Poincare inequalities associated with a
family of vector fields satisfying Hormander rank condition. Then, ap
plications are given to relative isoperimetric inequalities and to loc
al regularity (Harnack's inequality) for a class of degenerate ellipti
c equations with measurable coefficients.