EMBEDDING-THEOREMS AND THE HARNACK INEQUALITY FOR SOLUTIONS OF NONLINEAR SUBELLIPTIC EQUATIONS

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).