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

Series: 
PDE Seminar
Tuesday, November 25, 2014 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
Purdue University
 For a $C^{1,1}$-uniformly elliptic matrix $A$, let $H(x,p)=$ be the corresponding Hamiltonian function. Consider the Aronsson equation associated with $H$: $$(H(x,Du))x H_p(x,Du)=0.$$ In this talk, I will indicate everywhere differentiability of any viscosity solution of the above Aronsson's equation. This extends an important theorem by Evans and Smart on the infinity harmonic functions (i.e. $A$ is the identity matrix).