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The boundary Harnack principle for non-divergence form elliptic operators. (English) Zbl 0806.35025
Summary: If $$L$$ is a uniformly elliptic operator in non-divergence form, the boundary Harnack principle for the ratio of positive $$L$$-harmonic functions holds in Hölder domains of order $$\alpha$$ if $$\alpha>1/2$$. A counterexample shows that 1/2 is sharp. For Hölder domains of order $$\alpha$$ with $$\alpha \in (0,1]$$, the boundary Harnack principle holds provided the domain also satisfies a strong uniform regularity condition.

##### MSC:
 35J15 Second-order elliptic equations 35B45 A priori estimates in context of PDEs
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