一类Aronsson方程的黏性解的处处可微性
Everywhere differentiability of viscosity solutions to a class of Aronsson's equations
摘要：
对任意开集$Ω\subset\mathbb R^n$和$n\ge 2$，建立了Aronsson方程$$ <D_x(H(x, Du)), D_p H(x, Du)>=0 \quad \rm in\ \ Ω, $$的黏性解的处处可微性，其中$H$由$$H(x,\,p)=<A(x)p,p>=\sum_{i,\,j=1}^na^{ij}(x)p_i p_j,\ x\inΩ, \ p\in\mathbb R^n, $$给出，且$A=(a^{ij}(x))\in C^{1,1}(\barΩ,\mathbb R^{n\times n})$是一致椭圆的.这扩展了Evans和Smart \cite{es11a}关于无穷调和函数的一个较早的定理。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
