论文标题
退化schrödinger-type方程的平滑和Strichartz估计值
Smoothing and Strichartz estimates for degenerate Schrödinger-type equations
论文作者
论文摘要
在本文中，我们关注一些基本估计的schrödinger型运营商的有效性。一方面，我们通过适当的比较原则（我们将在此处获得）来得出任何顺序的运营商的全球同质平滑估计。另一方面，我们证明了时间分级的Scrhödinger操作员的加权strichartz型估计值，并将其应用于半线性库奇问题的当地良好性。我们的大多数结果也适用于非等级操作员，在这些情况下，恢复了众所周知的标准结果。
In this paper we focus on the validity of some fundamental estimates for time-degenerate Schrödinger-type operators. On one hand we derive global homogeneous smoothing estimates for operators of any order by means of suitable comparison principles (that we shall obtain here). On the other hand, we prove weighted Strichartz-type estimates for time-degenerate Scrhödinger operators and apply them to the local well-posedness of the semilinear Cauchy problem. Most of our results apply to nondegenerate operators as well, recovering, in these cases, the well-known standard results.
