On the regularity of solutions of the inhomogeneous infinity Laplace equation (Q2862190)

The paper deals with the regularity of solutions of an inhomogeneous infinity Laplace equation, in the unit ball \(B_1\): NEWLINE\[NEWLINE \begin{cases}\bigtriangleup_{\infty}u=u_{x_i}u_{x_j}u_{x_i x_j}=f &\text{in}\,\, \Omega \\ u=g & \text{on}\,\, \partial B_1 . \end{cases}NEWLINE\]NEWLINE with \(f \in L^{\infty}(B_1)\cap C^0(B_1)\) and \(g \in C^0(\partial B_1)\).NEWLINENEWLINEThe author proves that any blow-up is linear and it is non unique. Moreover, when the inomogeneity is \(C^1\) then the blow-up is unique and any solution is differentiable.