Everywhere differentiability of viscosity solutions to a class of Aronsson's equations

For any open set $Ω\subset\mathbb R^n$ and $n\ge 2$, we establish everywhere differentiability of viscosity solutions to the Aronsson equation $<D_x(H(x, Du)), D_p H(x, Du)>=0 \quad \rm in\ \ Ω,$ where $H$ is given by $H(x,\,p)=<A(x)p,p>=\sum_{i,\,j=1}^na^{ij}(x)p_i p_j,\ x\inΩ, \ p\in\mathbb R^n,$ and $A=(a^{ij}(x))\in C^{1,1}(\barΩ,\mathbb R^{n\times n})$ is uniformly elliptic. This extends an earlier theorem by Evans and Smart \cite{es11a} on infinity harmonic functions.

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