| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 36 | |
| Number of page(s) | 19 | |
| DOI | https://doi.org/10.1051/cocv/2020003 | |
| Published online | 25 June 2020 | |
Principal eigenvalues of fully nonlinear integro-differential elliptic equations with a drift term
1
Departamento de Matemática, Universidad Técnica Federico Santa María Casilla V-110, Avda. España,
1680 – Valparaíso, Chile.
2
CONICET Departamento de Matemática, FCEyN UBA Ciudad Universitaria,
Pab I (1428) Buenos Aires, Argentina.
3
Department of Mathematics, Jiangxi Normal University Nanchang,
Jiangxi
330022, PR China.
* Corresponding author: asalort@dm.uba.ar
Received:
20
July
2018
Accepted:
30
December
2019
We study existence of principal eigenvalues of a fully nonlinear integro-differential elliptic equations with a drift term via the Krein–Rutman theorem and regularity estimates up to boundary of viscosity solutions. We also show simplicity of eigenfunctions in the viscosity sense by using a nonlocal version of the ABP estimate and a “sweeping lemma”.
Mathematics Subject Classification: 35J60 / 47G20 / 35P30
Key words: Principal eigenvalue / integro-differential equation / regularity / Krein–Rutman theorem
© EDP Sciences, SMAI 2020
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