Uniqueness properties of degenerate elliptic operators

Let Omega be an open subset of R-d and K = -Sigma(d)(i,j=1) partial derivative(i)c(ij)partial derivative(j) + Sigma(d)(j=1) c(i)partial derivative(j) + c(0) a second-order partial differential operator with real-valued coefficients satisfying the strict ellipticity condition c = (c(ij)) > 0. Further let H = -Sigma(d)(i,j=1) partial derivative(i)c(ij)partial derivative(j) denote the principal part of K. Assuming an accretivity condition with C >= kappa (c circle times c(T)) with kappa > 0, an invariance condition (1(Omega), K-phi) = 0 and a growth condition which allows as parallel to C(x)parallel to similar to vertical bar x vertical bar(2) log vertical bar x vertical bar as vertical bar x vertical bar -> infinity we prove that K is L-1-unique if and only if H is L-1-unique or Markov unique.