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
2003-01-01
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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