Differential and Integral Equations

Gradient estimates and existence of mean curvature flow with transport term

Keisuke Takasao

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Abstract

In this paper we consider a hypersurface of the mean curvature flow with transport term when it is expressed by a graph. The existence of the mean curvature flow with transport term was proved by Liu, Sato, and Tonegawa [19] by using geometric measure theory. We give a proof of the gradient estimates and the short time existence for the mean curvature flow with transport term by applying the backward heat kernel.

Article information

Source
Differential Integral Equations, Volume 26, Number 1/2 (2013), 141-154.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1355867511

Mathematical Reviews number (MathSciNet)
MR3058702

Zentralblatt MATH identifier
1299.35183

Subjects
Primary: 35K93: Quasilinear parabolic equations with mean curvature operator 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

Citation

Takasao, Keisuke. Gradient estimates and existence of mean curvature flow with transport term. Differential Integral Equations 26 (2013), no. 1/2, 141--154. https://projecteuclid.org/euclid.die/1355867511


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