Abstract
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.
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References
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Święch, A. A note on the upper perturbation property and removable sets for fully nonlinear degenerate elliptic PDE. Nonlinear Differ. Equ. Appl. 26, 3 (2019). https://doi.org/10.1007/s00030-018-0547-1
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DOI: https://doi.org/10.1007/s00030-018-0547-1