Abstract
We study the prescribed mean curvature equation for nonparametric surfaces, obtaining existence and uniqueness results in the Sobolev space W 2, p . We also prove that under appropriate conditions the set of surfaces of mean curvature H is a connected subset of W 2, p . Moreover, we obtain existence results for a boundary value problem which generalizes the one-dimensional periodic problem for the mean curvature equation.
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More From: Nonlinear Analysis: Theory, Methods & Applications
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