Solutions of Aronsson Equation near Isolated Points
نویسنده
چکیده
When n ≥ 2, we show that for a non-negative solution of the Aronsson equation AH(u) = DxH(Du(x)) · Hp(Du(x)) = 0 an isolated singularity x0 is either a removable singularity or u(x) = b+CH k (x− x0)+ o(|x− x0|) ( or u(x) = b−C Ĥ k (x− x0)+ o(|x− x0|) ) for some k > 0 and b ∈ R . Here CH k and C Ĥ k are general cone functions. This generalizes the asymptotic behavior theory for infinity harmonic functions by Savin, Wang and Yu [14]. The Hamiltonian H ∈ C2(Rn) is assumed to be non-negative and uniformly convex.
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