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

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

2 Scopus Citations
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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)2708-2736
Journal / PublicationJournal of Differential Equations
Volume264
Issue number4
Online published13 Nov 2017
Publication statusPublished - 15 Feb 2018
Externally publishedYes

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.

Research Area(s)

  • Aleksandrov–Bakelman–Pucci maximum principle, Integro-PDE