Abstract
The aim of this thesis is to derive new gradient estimates for parabolic equations. The gradient estimates found are independent of the regularity of the initial data. This allows us to prove the existence of solutions to problems that have non-smooth, continuous initial data. We include existence proofs for problems with both Neumann and Dirichlet boundary data. The class of equations studied is modelled on mean curvature flow for graphs. It includes anisotropic mean curvature flow, and other operators that have no uniform non-degeneracy bound. We arrive at similar estimates by three different paths: a 'double coordinate' approach, an approach examining the intersections of a solution and a given barrier, and a classical geometric approach.
Paper version not known (
Free)
Published Version
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 callDisclaimer: 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.
