The mean curvature measure (Q2428718)

The authors study the existence of weak solutions of the Dirichlet problem of the mean curvature equation \(H_1[u]=\nu\) when \(\nu\) is a measure. They assign a measure to upper semicontinuous functions, consider the \(H_1\)-subharmonic functions and obtain the weak convergence for this measure. The authors also derive the weak continuity of the mean curvature operator by using the crucial Harnack inequality.