Internet Archive Scholar

Viscosity solutions for the crystalline mean curvature flow with a nonuniform driving force term

Yoshikazu Giga, Norbert Požár
2020 SN Partial Differential Equations and Applications  

Preserved Fulltext

fulltext thumbnail
Web Archive Capture PDF (1.1 MB)
https://web.archive.org/web/20210429093731/https://link.springer.com/content/pdf/10.1007/s42985-020-00040-0.pdf?error=cookies_not_supported&code=d2b61716-53f5-4be8-99c7-29900d744798

A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL. The file type is application/pdf.

A general purely crystalline mean curvature flow equation with a nonuniform driving force term is considered. The unique existence of a level set flow is established when the driving force term is continuous and spatially Lipschitz uniformly in time. By introducing a suitable notion of a solution a comparison principle of continuous solutions is established for equations including the level set equations. An existence of a solution is obtained by stability and approximation by smoother
more » ... A necessary equi-continuity of approximate solutions is established. It should be noted that the value of crystalline curvature may depend not only on the geometry of evolving surfaces but also on the driving force if it is spatially inhomogeneous.
doi:10.1007/s42985-020-00040-0 fatcat:mywqj23iibhbxeoegnzzmokyxa
Open Access
Citation

Yoshikazu Giga, Norbert Požár. "Viscosity solutions for the crystalline mean curvature flow with a nonuniform driving force term." SN Partial Differential Equations and Applications 1.6 (2020)