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

  • Andrzej ŚwięchEmail author
Article
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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.

Keywords

Viscosity solution \(L^n\)-viscosity solution Fully non-linear elliptic PDE 

Mathematics Subject Classification

35D40 35J15 35J60 35J70 35K10 35K55 35K65 

Notes

References

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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