Existence of Curvature Flow with Forcing in a Critical Sobolev Space
Abstract
Suppose that a closed 1-rectifiable set $Γ_0\subset\mathbb R^2$ of finite 1-dimensional Hausdorff measure and a vector field $u$ in a dimensionally critical Sobolev space are given. It is proved that, starting from $Γ_0$, there exists a non-trivial flow of curves with the normal velocity given by the sum of the curvature and the given vector field $u$. The motion law is satisfied in the sense of Brakke and the flow exists through singularities.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Advanced Mathematical Physics Problems
Publication details
- Journal / source
- ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
- Publisher
- Scuola Normale Superiore - Edizioni della Normale
- Pages
- 28–28
- Publication date
- 17 August 2026
- Language
- EN