L. Capogna et al., EMBEDDING-THEOREMS AND THE HARNACK INEQUALITY FOR SOLUTIONS OF NONLINEAR SUBELLIPTIC EQUATIONS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 316(8), 1993, pp. 809-814
We consider a class of nonlinear sub-elliptic equations whose model is
given by SIGMA(j=1)m X(j)(\D(L)u\p-2 X(j)u)=0, 1<p<infinity. Here, X
1,...,X(m) are C(infinity) vector fields satisfying Hormander's hypoel
lipticity condition and X(j) denotes the formal adjoint of X(j). We p
rove an optimal imbedding theorem of Sobolev type and a uniform Harnac
k inequality with respect to the metric associated to X1,...,X(m).