Abstract
We study some properties of graphs whose mean curvature (in distributional sense) is a vector Radon measure. In particular, we prove that the distributional mean curvature of the graph of a Lipschitz continuous function u is a measure if and only if the distributional divergence of T u is a measure. This equivalence fails to be true if Lipschitz continuity is relaxed, as it is shown in a couple of examples. Finally, we prove a theorem of approximation in W (1,1) and in the sense of mean curvature of C 2 graphs by polyhedral graphs. A number of examples illustrating different situations which can occur complete the work.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore 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.
