Evolution of Nonparametric Surfaces with Speed Depending on Curvature, III. Some Remarks on Mean Curvature and Anisotropic flows
Evolution of Nonparametric Surfaces with Speed Depending on Curvature, III. Some Remarks on Mean Curvature and Anisotropic flows
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非参数曲面的演化速度取决于曲率，III。
DOI：
10.1007/978-1-4612-0885-3_10
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
N. Uraltseva
中科院分区：
文献类型：
--
作者：
V. Oliker;N. Uraltseva
This paper is a sequel to our paper [OU] where we investigated questions concerning solvability and asymptotic behavior of solutions to the mean curvature evolution problem
$$ {u_t} = \sqrt {1 + {{\left| {Du} \right|}^2}} H\left( u \right)\;in\quad \Omega \times \left( {0,\infty } \right),$$
(1.1)
$$ u\left( {x,t} \right) = 0\quad on\quad \partial \Omega \times \left[ {0,\infty } \right),$$
(1.2)
$$ u\left( {x,0} \right) = {u_0}\left( x \right)\quad in\quad \overline {\Omega ,} \quad {u_0} \in C_0^\infty \left( {\overline \Omega } \right)$$
(1.3)
where Ω is a bounded domain in R n , n ≥ 2, with C∞ boundary ∂Ω, H is the mean curvature operator.
This paper is a sequel to our paper [OU] where we investigated questions concerning solvability and asymptotic behavior of solutions to the mean curvature evolution problem
$$ {u_t} = \sqrt {1 + {{\left| {Du} \right|}^2}} H\left( u \right)\;in\quad \Omega \times \left( {0,\infty } \right),$$
(1.1)
$$ u\left( {x,t} \right) = 0\quad on\quad \partial \Omega \times \left[ {0,\infty } \right),$$
(1.2)
$$ u\left( {x,0} \right) = {u_0}\left( x \right)\quad in\quad \overline {\Omega ,} \quad {u_0} \in C_0^\infty \left( {\overline \Omega } \right)$$
(1.3)
where Ω is a bounded domain in R n , n ≥ 2, with C∞ boundary ∂Ω, H is the mean curvature operator.