Comparison principles for p-Laplace equations with lower order terms

We prove comparison principles for quasilinear elliptic equations whose simplest model is λ u - Δ p u + H ( x , D u ) = 0 x ∈ Ω , where Δ p u = div ( | D u | p - 2 D u ) is the p -Laplace operator with p > 2 , λ ≥ 0 , H ( x , ξ ) : Ω × R N → R is a Carathéodory function and Ω ⊂ R N is a bounded d...

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2017-06, Vol.196 (3), p.877-903
Main Authors: Leonori, Tommaso, Porretta, Alessio, Riey, Giuseppe
Format: Article
Language:English
Subjects:
Elliptic functions
Laplace equation
Mathematics
Mathematics and Statistics
Principles
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Summary:We prove comparison principles for quasilinear elliptic equations whose simplest model is λ u - Δ p u + H ( x , D u ) = 0 x ∈ Ω , where Δ p u = div ( | D u | p - 2 D u ) is the p -Laplace operator with p > 2 , λ ≥ 0 , H ( x , ξ ) : Ω × R N → R is a Carathéodory function and Ω ⊂ R N is a bounded domain, N ≥ 2 . We collect several comparison results for weak sub- and super-solutions under different setting of assumptions and with possibly different methods. A strong comparison result is also proved for more regular solutions.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-016-0600-9