Estimates of Green functions and harmonic measures for elliptic operators with singular drift terms

In this paper, we prove the existence and uniqueness of the continuous Green function G for the elliptic operator L = div(A(x)∇x)+B(x)·∇x with singular drift term B on a C1,1 bounded domain D in Rn, n ≥ 3, and its comparability to the Green function G0 of L0 = div(A(x)∇x). Basing on this result we establish the equivalence of the L-harmonic measure and the surface measure on ∂D. These results extend some first ones proved for elliptic operators with less singular drift terms

Estimates of Green functions and harmonic measures for elliptic operators with singular drift terms

In this paper, we prove the existence and uniqueness of the continuous Green function G for the elliptic operator L = div(A(x)∇x)+B(x)·∇x with singular drift term B on a C1,1 bounded domain D in Rn, n ≥ 3, and its comparability to the Green function G0 of L0 = div(A(x)∇x). Basing on this result we establish the equivalence of the L-harmonic measure and the surface measure on ∂D. These results extend some first ones proved for elliptic operators with less singular drift terms