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

页码：341 / 359

页数：19

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