Generalized Harnack inequality for semilinear elliptic equations
Julin, V. (2016). Generalized Harnack inequality for semilinear elliptic equations. Journal de Mathématiques Pures et Appliquées, 106 (5), 877-904. doi:10.1016/j.matpur.2016.03.015
Published inJournal de Mathématiques Pures et Appliquées
© 2016 Elsevier Masson SAS. This is a final draft version of an article whose final and definitive form has been published by Elsevier. Published in this repository with the kind permission of the publisher.
This paper is concerned with semilinear equations in divergence form div(A(x)Du) = f(u) where f : R → [0, ∞) is nondecreasing. We introduce a sharp Harnack type inequality for nonnegative solutions which is a quantified version of the condition for strong maximum principle found by Vazquez and Pucci-Serrin in [30, 24] and is closely related to the classical Keller-Osserman condition [15, 22] for the existence of entire solutions.