Interior W1,p Regularity and Holder Continuity of Weak Solutions to a Class of Divergence Kolmogorov Equations with Discontinuous Coefficients

We consider a class of Kolmogorov equation Lu = Sigma(p0)(i,j=1) partial derivative(xi) (a(ij) (z) partial derivative(xj)u) + Sigma(N)(i,j=1) b(ij)x(i)partial derivative(xj)u - partial derivative(t)u = Sigma(p0)(j=1) partial derivative x(j) F-j (z) in a bounded open domain Omega subset of RN+1, where the coefficients matrix (a (ij) (z)) is symmetric uniformly positive definite on . We obtain interior W (1,p) (1 < p < a) regularity and Holder continuity of weak solutions to the equation under the assumption that coefficients a (ij) (z) belong to the and is a constant matrix such that the frozen operator is hypoelliptic.