Asymptotics for the level set equation near a maximum-Reference-Cited by-同舟云学术

Asymptotics for the level set equation near a maximum

Published:2020-06-01 Issue:763 Volume:2020 Page:201-221
ISSN:1435-5345
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:
Short-container-title:

Author:

Strehlke Nicholas¹

Affiliation:

1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Abstract

AbstractWe give asymptotics for the level set equation for mean curvature flow on a convex domain near the point where it attains a maximum. It is known that solutions are not necessarily

{C^{3}}

, and we recover this result and construct non-smooth solutions which are

{C^{3}}

. We also construct solutions having prescribed behavior near the maximum. We do this by analyzing the asymptotics for rescaled mean curvature flow converging to a stationary sphere.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2018-0033/pdf

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