A note on the Harnack inequality for elliptic equations in divergence form (Q2832814)

This note rephrases the proof of the Harnack inequality for the solutions of uniformly elliptic equations of second order in the divergence form \(\nabla\cdot (a\nabla u)=0\) in cubes. The proof relies on two key points that are consequence of two De Giorgi results. One is a local maximum principle in which it is applied the interpolation argument. Another is a weak Harnack inequality in which it is applied the induction argument and it is taken the Calderón-Zygmund cube decomposition into account.