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 in
Journal de Mathématiques Pures et AppliquéesDate
2016Discipline
MatematiikkaCopyright
© 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.