THE BOUNDARY HARNACK PRINCIPLE FO NON-DIVERGENCE FROM ELLIPTIC-OPERATORS

If L is a uniformly elliptic operator in non-divergence form, the boun dary Harnack principle for the ratio of positive L-harmonic functions holds in Holder domains of order alpha if alpha > 1/2. A counterexampl e shows that 1/2 is sharp. For Holder domains of order alpha with alph a is-an-element-of (0,1], the boundary Harnack principle holds provide d the domain also satisfies a strong uniform regularity condition.