Coherence on Fractals Versus Pointwise Convergence for the Schrodinger Equation

被引：35
|
作者：
Luca, Renato [1 ]
Rogers, Keith M. [1 ]
机构：
[1] CSIC UAM UC3M UCM, Inst Ciencias Matemat, Madrid 28049, Spain
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2017年 / 351卷 / 01期
关键词：
DIVERGENCE SETS;
D O I：
10.1007/s00220-016-2722-8
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We consider Carleson's problem regarding convergence for the Schrodinger equation in dimensions d >= 2. We show that if the solution converges almost everywhere with respect to alpha-Hausdorff measure to its initial datum as time tends to zero, for all data H-s (R-d), then s >= d/2(d+2)( d + 1 - alpha). This strengthens and generalises results of Bourgain and Dahlberg-Kenig.
引用
收藏
页码：341 / 359
页数：19
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