A Free Boundary Problem for Minimal Surface Equation
Yoshihiko Yamaura · Institutional Repositories DataBase (IRDB) · 1991
In this note we introduced a free boundary problem for minimal surface equation. The following variational problem had been treated by H.W.Alt, L.A.Caffarelli and A.Freedman $[1],[2] $: $\\{\\begin{array}{l}\\int_{\\Omega}(F(|\ abla u|^{2})+Q^{2}\\chi_{u>0})dL^{n}arrow\\min u\\in IC\\equiv\\{w\\in L_{1oc}^{2}(\\Omega)|\ abla w\\in L^{2}(\\Omega),w=u^{0}on S\\}\\end{array} $ (1.1) where $\\Omega $ is a connected Lipshitz domain contained in n-dimensional Euclidean space $R$“. $F=F(t) $ is a