Supersolutions to nonautonomous Choquard equations in general domains

We consider the nonlocal quasilinear elliptic problem: where is a smooth domain in , , , , stands for the Riesz potential, , , are monotone nondecreasing functions with for , and are nonnegative measurable functions. We provide explicit quantitative pointwise estimates on positive weak supersolution...

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Bibliographic Details
Published in:Advances in nonlinear analysis 2023-10, Vol.12 (1), p.423-443
Main Authors: Aghajani, Asadollah, Kinnunen, Juha
Format: Article
Language:English
Subjects:
35A23
35B09
35B53
35J92
47J10
eigenvalue problems
Laplace operator
Liouville-type theorems
m-laplace operator
quasilinear elliptic equations
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Summary:We consider the nonlocal quasilinear elliptic problem: where is a smooth domain in , , , , stands for the Riesz potential, , , are monotone nondecreasing functions with for , and are nonnegative measurable functions. We provide explicit quantitative pointwise estimates on positive weak supersolutions. As an application, we obtain bounds on extremal parameters of the related nonlinear eigenvalue problems in bounded domains for various nonlinearities and such as , and , . We also discuss the Liouville-type results in unbounded domains.
ISSN:2191-950X
2191-950X
DOI:10.1515/anona-2023-0107