The Dirichlet problem for the minimal surface equation on unbounded planar domains (Q910706)

We prove existence and regularity results depending on the boundary data f (or g) for solutions u (or v) of the minimal surface equation on a certain unbounded domain \(\Omega\). Suppose \(\Omega\) is convex and contained in a band or proper sector, if f, g are uniformly continuous and bounded on \(\partial \Omega\) then so is the solution u, v, respect. This also holds for ``convex city maps''. If f-g\(\leq A\) on \(\partial \Omega\) then u-v\(\leq A\) on \(\Omega\). Our techniques can be generalized to \(\Omega \subset R^ n\) (this is part of a joint work appearing in Proc. in Honor to M. do Carmo). Main generalizations for the mean curvature equation has been done by \textit{Collin} and \textit{R. Krust} (to appear in Bull. Soc. Math. Fr.), and by \textit{J.-F. Hwang} [Ann. Sc. Norm. Super Pisa, Cl. Sci., IV. Ser. 15, No.3, 341-355 (1988)].