The prescribed mean curvature equation for nonparametric surfaces

✍ Scribed by P. Amster; M.C. Mariani

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 112 KB
• Volume: 52
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(02)00105-0

✦ Synopsis

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.