This paper is concerned with the maximum principle for subsolutions of second-order linear elliptic equations in non-divergence form. We give a proof of the Hopf maximum principle based on a weak Harnack inequality which extends to weakly differentiable functions and show conditions in order the weak maximum principle and the Alexandroff-Bakelman-Pucci estimate to hold in any unbounded domain.
Remarks on the maximum principle and uniqueness estimates
VITOLO, Antonio
2003
Abstract
This paper is concerned with the maximum principle for subsolutions of second-order linear elliptic equations in non-divergence form. We give a proof of the Hopf maximum principle based on a weak Harnack inequality which extends to weakly differentiable functions and show conditions in order the weak maximum principle and the Alexandroff-Bakelman-Pucci estimate to hold in any unbounded domain.File in questo prodotto:
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