A short proof of boundary Harnack principle (Q2180553)

The authors give a short proof of the classical Boundary Harnack Principle for solutions to linear uniformly elliptic equations. It is extremely interesting that their proof gives a unified approach for both divergence and non-divergence linear equations. Their approch does not make use of the Green's function. The idea is to find an ``almost positivity property'' of a solution, which can be iterated from scale one to all smaller scales. The same strategy also applies to other similar situations. The key property of uniformly elliptic equations needed in their proof is a suitable Weak Harnack Inequality for subsolutions, which holds for both divergence and non-divergence equations.