The prescribed mean curvature equation for nonparametric surfaces Original Research Article

We study the prescribed mean curvature equation for nonparametric surfaces, obtaining existence and uniqueness results in the Sobolev space W2,p. We also prove that under appropriate conditions the set of surfaces of mean curvature H is a connected subset of W2,p. Moreover, we obtain existence results for a boundary value problem which generalizes the one-dimensional periodic problem for the mean curvature equation.