Aleksandrov–Bakelman–Pucci maximum principles for a class of uniformly elliptic and parabolic integro-PDE

Chenchen Mou; Andrzej Święch

doi:10.1016/j.jde.2017.11.004

Aleksandrov–Bakelman–Pucci maximum principles for a class of uniformly elliptic and parabolic integro-PDE

Chenchen Mou^*, Andrzej Święch

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

6 Citations (Scopus)

Abstract

We prove generalized Aleksandrov–Bakelman–Pucci maximum principles for elliptic and parabolic integro-PDEs of Hamilton–Jacobi–Bellman–Isaacs types, whose PDE parts are either uniformly elliptic or uniformly parabolic. The proofs of these results are based on the classical Aleksandrov–Bakelman–Pucci maximum principles for the elliptic and parabolic PDEs and an iteration procedure using solutions of Pucci extremal equations. We also provide proofs of nonlocal versions of the classical Aleksandrov–Bakelman–Pucci maximum principles for elliptic and parabolic integro-PDEs.

Original language	English
Pages (from-to)	2708-2736
Journal	Journal of Differential Equations
Volume	264
Issue number	4
Online published	13 Nov 2017
DOIs	https://doi.org/10.1016/j.jde.2017.11.004
Publication status	Published - 15 Feb 2018
Externally published	Yes

Research Keywords

Aleksandrov–Bakelman–Pucci maximum principle
Integro-PDE

Access Output

10.1016/j.jde.2017.11.004Licence: Elsevier user license

Other Access Options

Check CityUHK Library

Permanent Link

Right click to copy link

Cite this

@article{7b63a905434141baba6034c281dd65cc,

title = "Aleksandrov–Bakelman–Pucci maximum principles for a class of uniformly elliptic and parabolic integro-PDE",

abstract = "We prove generalized Aleksandrov–Bakelman–Pucci maximum principles for elliptic and parabolic integro-PDEs of Hamilton–Jacobi–Bellman–Isaacs types, whose PDE parts are either uniformly elliptic or uniformly parabolic. The proofs of these results are based on the classical Aleksandrov–Bakelman–Pucci maximum principles for the elliptic and parabolic PDEs and an iteration procedure using solutions of Pucci extremal equations. We also provide proofs of nonlocal versions of the classical Aleksandrov–Bakelman–Pucci maximum principles for elliptic and parabolic integro-PDEs.",

keywords = "Aleksandrov–Bakelman–Pucci maximum principle, Integro-PDE, Aleksandrov–Bakelman–Pucci maximum principle, Integro-PDE, Aleksandrov–Bakelman–Pucci maximum principle, Integro-PDE",

author = "Chenchen Mou and Andrzej {\'S}wi{\c e}ch",

year = "2018",

month = feb,

day = "15",

doi = "10.1016/j.jde.2017.11.004",

language = "English",

volume = "264",

pages = "2708--2736",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "4",

}

TY - JOUR

T1 - Aleksandrov–Bakelman–Pucci maximum principles for a class of uniformly elliptic and parabolic integro-PDE

AU - Mou, Chenchen

AU - Święch, Andrzej

PY - 2018/2/15

Y1 - 2018/2/15

N2 - We prove generalized Aleksandrov–Bakelman–Pucci maximum principles for elliptic and parabolic integro-PDEs of Hamilton–Jacobi–Bellman–Isaacs types, whose PDE parts are either uniformly elliptic or uniformly parabolic. The proofs of these results are based on the classical Aleksandrov–Bakelman–Pucci maximum principles for the elliptic and parabolic PDEs and an iteration procedure using solutions of Pucci extremal equations. We also provide proofs of nonlocal versions of the classical Aleksandrov–Bakelman–Pucci maximum principles for elliptic and parabolic integro-PDEs.

AB - We prove generalized Aleksandrov–Bakelman–Pucci maximum principles for elliptic and parabolic integro-PDEs of Hamilton–Jacobi–Bellman–Isaacs types, whose PDE parts are either uniformly elliptic or uniformly parabolic. The proofs of these results are based on the classical Aleksandrov–Bakelman–Pucci maximum principles for the elliptic and parabolic PDEs and an iteration procedure using solutions of Pucci extremal equations. We also provide proofs of nonlocal versions of the classical Aleksandrov–Bakelman–Pucci maximum principles for elliptic and parabolic integro-PDEs.

KW - Aleksandrov–Bakelman–Pucci maximum principle

KW - Integro-PDE

KW - Aleksandrov–Bakelman–Pucci maximum principle

KW - Integro-PDE

KW - Aleksandrov–Bakelman–Pucci maximum principle

KW - Integro-PDE

UR - http://www.scopus.com/inward/record.url?scp=85034609599&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85034609599&origin=recordpage

U2 - 10.1016/j.jde.2017.11.004

DO - 10.1016/j.jde.2017.11.004

M3 - RGC 21 - Publication in refereed journal

SN - 0022-0396

VL - 264

SP - 2708

EP - 2736

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 4

ER -

Aleksandrov–Bakelman–Pucci maximum principles for a class of uniformly elliptic and parabolic integro-PDE

Abstract

Research Keywords

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Corrigendum to “Aleksandrov–Bakelman–Pucci maximum principles for a class of uniformly elliptic and parabolic integro-PDE” [J. Differential Equations 264 (2018) 2708–2736]

Cite this