Viscosity solutions to inhomogeneous Aronsson's equations involving Hamiltonians ⟨A(x)p,p⟩.

We consider inhomogeneous Aronsson's equation where U is a bounded domain of Rn with n≥2, A∈C1(U;Rn×n) is symmetric and uniformly elliptic, and f∈C(U). First, we establish the existence and uniqueness of viscosity solutions for the corresponding Dirichlet problem on subdomains. Then we obtain the local Lipschitz regularity and the linear approximation property of viscosity solutions to (0.1). Moreover, under additional assumptions that A∈C1,1(U;Rn×n) and f∈C0,1(U), we prove the everywhere differentiability of viscosity solutions to (0.1). [ABSTRACT FROM AUTHOR]