| Abstract: |
| We present several classical regularity estimates for general uniformly elliptic operators of second order in divergence form and unbounded coefficients, giving explicit and optimal dependence of the constants in these inequalities in terms of Lebesgue norms of the lower order coefficients of the operator, and the size of the domain. Among these estimates are the interior and global Harnack inequalities, the Hopf lemma, $L^\infty$-estimates, and logarithmic gradient estimates. Applications include the Landis conjecture and the Vazquez strong maximum principle for operators with unbounded coefficients. |
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