Existence of selfsimilar shrinking curves for anisotropic curvature flow equations
Existence of selfsimilar shrinking curves for anisotropic curvature flow equations
复制标题
DOI：
10.1007/bf01189949
复制
发表时间：
1994-03
影响因子：
2.1
通讯作者：
C. Dohmen;Y. Giga;N. Mizoguchi
中科院分区：
文献类型：
--
作者：
C. Dohmen;Y. Giga;N. Mizoguchi
在R（1.1）u中，对于给定的正函数a，Uxx+ u-~= 0.这个方程是在描述各向异性曲率流方程的自相似解时产生的。由于x是曲线法线的辐角，所以很自然地对（1.1）中的a施加27 r-周期性，并要求存在27 r-周期解。为了简化符号，我们注意到27 r-周期函数可以被视为平坦环面T：= R/27 rZ上的函数。例如，空间Cm（T）是R上所有27 r-周期Cm-函数的空间。设Cm（T）表示Cm（T）中所有正函数的集合.特别是
Uxx+ u-~= 0 inR(1.1) u with a given positive function a. This equation arises in describing a selfsimilar solution of anisotropic curvature flow equations. Since x is the argument of the normal of the curve it is natural to impose 27r-periodicity for a in (1.1) and to ask for existence of 27r-periodic solutions. To simplify the notation we notice that a 27r-periodic function can be regarded as a function on the flat torus T:= R/27rZ. For example the space Cm (T) is the space of all 27r-periodic C m-functions on R. Let Cm (T) denote the set of all positive functions in Cm (T). In particular