Abstract
We study surfaces of prescribed bounded mean curvature H in a partially free boundary configuration \(\langle\Gamma,{\cal S}\rangle\). If \(\Gamma\) is projectable onto and \(\) is a cylinder surface over the x1,x2-plane, we show that also the spanned H-surface \({\bf x}\) is projectable onto this plane. Besides certain conditions on \(\langle\Gamma,{\cal S}\rangle\) and H, we have to suppose that \({\bf x}\) is stationary and freely stable w.r.t. the generalized area functional \(A_{{\bf Q}}({\bf x})\), and the vector field \({\bf Q}={\bf Q}({\bf x})\) is assumed to be tangential on \({\cal S}\). Consequences are uniqueness of freely stable H-surfaces and solvability of a mixed boundary problem for the nonparametric prescribed mean curvature equation.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Calculus of Variations and Partial Differential Equations
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.