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Braga, J. Ederson M.; Moreira, Diego
Nonlinear differential equations and applications, 04/2018, Letnik: 25, Številka: 2Journal Article
Our main result in this note can be stated as follows: Assume E ⊂ B 1 and 0.1 F ( D 2 u ( x ) , ∇ u ( x ) , u ( x ) , x ) ≤ ψ ( x ) in B 1 \ E holds in the C - viscosity sense where | E | = 0 and F is a degenerate elliptic operator. This way, ( 0.1 ) holds in the whole unit ball B 1 (i.e, E is removable for ( 0.1 )) provided 0.2 M λ , Λ - ( D 2 u ) - γ | ∇ u | ≤ f in B 1 where f ∈ L n ( B 1 ) . Zeroth order term can appear in ( 0.2 ) provided u is bounded in B 1 . This extends a result due to Caffarelli et al. proven in (Commun Pure Appl Math 66(1):109–143, 2013 ) where a second order linear uniformly elliptic PDE with bounded RHS appeared in place of ( 0.2 ).
