On the ABP maximum principle for $L^p$-viscosity solutions of fully nonlinear PDE

Koike, Shigeaki

doi:10.2969/aspm/06410113

VOL. 64 | 2015 On the ABP maximum principle for $L^p$-viscosity solutions of fully nonlinear PDE

Shigeaki Koike

Editor(s) Shin-Ichiro Ei, Shuichi Kawashima, Masato Kimura, Tetsu Mizumachi

Adv. Stud. Pure Math., 2015: 113-124 (2015) DOI: 10.2969/aspm/06410113

Abstract

Fully nonlinear second-order uniformly elliptic partial differential equations (PDE for short) with unbounded ingredietns are considered. The Aleksandrov–Bakelman–Pucci (ABP for short) maximum principle for $L^p$-viscosity solutions of fully nonlinear, second-order uniformly elliptic PDE are shown.

The results here are joint works with A. Świȩch in [12], [13], [14], [15].