6533b824fe1ef96bd1280258
RESEARCH PRODUCT
Generalized Harnack inequality for semilinear elliptic equations
Vesa Julinsubject
Pure mathematicsHarnack inequalitynonhomogeneous equationsApplied MathematicsGeneral Mathematicsta111010102 general mathematicselliptic equations in divergence formsemilinear equationsMathematics::Analysis of PDEsType inequality01 natural sciences010101 applied mathematicsMaximum principleMathematics - Analysis of PDEsFOS: MathematicsMathematics::Differential Geometry0101 mathematicsDivergence (statistics)MathematicsHarnack's inequalityAnalysis of PDEs (math.AP)description
Abstract This paper is concerned with semilinear equations in divergence form div ( A ( x ) D u ) = 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-04-23 |