Uniqueness properties of degenerate elliptic operators

Let Ω be an open subset of R ^d and a second-order partial differential operator with real-valued coefficients satisfying the strict ellipticity condition C = (c _ij) > 0. Further let denote the principal part of K. Assuming an accretivity condition with κ > 0, an invariance condition and a growth condition which allows {double pipe}C(x){double pipe} ~ {pipe}x{pipe} ² log{pipe}x{pipe} as {pipe}x{pipe} → ∞ we prove that K is L ₁-unique if and only if H is L ₁-unique or Markov unique.