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C^1 regularity of the Aronsson equation in R^2
PDE Seminar| Speaker: | Professor Changyou Wang, University of Kentucky |
| Location: | 693 Kerr |
| Start time: | Thu, Nov 10 2005, 3:10PM |
Consider the two dimensional Aronsson equation: $$H_{p_i}(Du)H_{p_j}(Du) u_{ij}=0, in R^2$$ we prove that if $H$ is $C^2$, strictly convex, then any continuous viscosity solution of the Aronsson equation is $C^1$. It extends the corresponding theorem on infinity harmonic function by Savin. This is joint work with Yifeng Yu from UT Austin