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A note on the upper perturbation property and removable sets for fully nonlinear degenerate elliptic PDE

The purpose of this short note is to attract attention to the concept of the upper perturbation property of L n -viscosity subsolutions introduced in Crandall et al. (in: On the equivalence of various weak notions of solutions of elliptic PDEs with measurable ingredients, progress in elliptic and pa...

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Published in:Nonlinear differential equations and applications 2019-02, Vol.26 (1), p.1-4, Article Paper No. 3, 4
Main Author: Święch, Andrzej
Format: Article
Language:English
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Summary:The purpose of this short note is to attract attention to the concept of the upper perturbation property of L n -viscosity subsolutions introduced in Crandall et al. (in: On the equivalence of various weak notions of solutions of elliptic PDEs with measurable ingredients, progress in elliptic and parabolic partial differential equations (Capri, 1994), Longman, Harlow, 1996 ). We show that a recent result of Braga and Moreira (NoDEA Nonlinear Differ Equ Appl 25(2):12, 2018 ) about removable sets for viscosity solutions of fully nonlinear degenerate elliptic PDE is an easy consequence of the upper perturbation property. We also prove a parabolic result about removable sets.
ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-018-0547-1