ERC Workshop on Geometric Measure Theory, Analysis in Metric Spaces and Real Analysis

Existence and regularity of mean curvature flow with transport term

speaker: Yoshihiro Tonegawa (Hokkaido University)

abstract: We consider the following problem. Suppose on \(\mathbb R^n\) (\(2\leq n\)) that we are given a vector field \(u\) and a bounded \(C^1\) hypersurface \(M_0\). Prove the existence and regularity of a family of hypersurfaces \(\{M_t\}_{t>0}\) starting from \(M_0\) such that the normal velocity of \(M_t\) is equal to \(h+u^{\perp}\), where \(u^{\perp}\) is the normal projection of \(u\). When \(u=0\), it is the usual mean curvature flow (MCF). If \[u\in L^q_{loc}([0,\infty);W^{1,p}({\mathbb R}^n))\] with \(2
timetable:
Thu 10 Oct, 10:00 - 10:50, Aula Dini
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