分野別セミナー

We prove the unique solvability of higher order curvature flow
equations with rough initial data. To be more precise, we prove
the unique existence of solutions of the surface diffusion flow
and the Willmore flow, with an initial curve whose curvature is
not necessarily continuous. For this purpose we develop an
abstract theory for quasilinear parabolic equations based on the
theory of analytic semigroups.