论文标题
log-lipschitz系数
Subelliptic Wave Equations with Log-Lipschitz coefficients
论文作者
论文摘要
在本文中，我们研究了紧凑型谎言组的左不变矢量场和不变矢量场和低纤维均质均匀左右不变的差分差算子（正岩石运算符）的较差的矢量磁场（正相关），当时依赖性传播速度满足对数ligipschitz条件时，我们证明了相关的Sobolev空间中的良好性，相对于初始数据表现出有限的规律性丧失，当传播速度为$ {\ rm H \ ddot {o} lder} $函数时，这是不正确的。我们还指出了希尔伯特将军的扩展。在$ \ mathbb r^n $的Laplacian的特殊情况下，结果归结为Colombini-de Giorgi和Spagnolo的著名结果。
In this paper we study the Cauchy problem for the wave equations for sums of squares of left invariant vector fields on compact Lie groups and also for hypoelliptic homogeneous left-invariant differential operators on graded Lie groups (the positive Rockland operators), when the time-dependent propagation speed satisfies a Log-Lipschitz condition. We prove the well-posedness in the associated Sobolev spaces exhibiting a finite loss of regularity with respect to the initial data, which is not true when the propagation speed is a ${\rm H\ddot{o}lder}$ function. We also indicate an extension to general Hilbert spaces. In the special case of the Laplacian on $\mathbb R^n$, the results boil down to the celebrated result of Colombini-De Giorgi and Spagnolo.
