The prescribed mean curvature equation for nonparametric surfaces |
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| Institution: | 1. Department of Mathematics, Indian Institute of Technology–Madras, Chennai, India;2. Departamento de Matemáticas, Universidad de los Andes, Bogotá, Colombia;1. Department of Nuclear and Particle Physics, Faculty of Physics, National and Kapodistrian University of Athens, 15784 Athens, Greece;2. Theoretical Physics Department, CERN, 1211 Geneva 23, Switzerland |
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| Abstract: | 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. |
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