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Jul 18, 2018 at 14:46 comment added Jeff If you want a reference that is easier to digest than the user's guide, I would suggest Crandall's paper "Viscosity Solutions: A primer". His results are not as general as in the user's guide, but it does cover your equation and is easier to follow (in my opinion).
Jul 18, 2018 at 8:45 comment added mnmn1993 Thank you so much for your detailed answer! The construction of the subsolution can be strict in the my equation. May I have a good reference of the proof of Theorem 3.3 (the comparison principle) in user's guide?
Jul 18, 2018 at 8:34 vote accept mnmn1993
Jul 17, 2018 at 17:31 history answered Jeff CC BY-SA 4.0