Convergence over fractals for the Schroedinger equation

IF 1.2 2区数学 Q1 MATHEMATICS

Indiana University Mathematics Journal Pub Date : 2021-01-07 DOI:10.1512/iumj.2022.71.9302

R. Lucà, F. Ponce-Vanegas

引用次数: 3

Abstract

We consider a fractal refinement of the Carleson problem for the Schr\"odinger equation, that is to identify the minimal regularity needed by the solutions to converge pointwise to their initial data almost everywhere with respect to the $\alpha$-Hausdorff measure ($\alpha$-a.e.). We extend to the fractal setting ($\alpha

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薛定谔方程的分形收敛性

我们考虑对Schrödinger方程的Carleson问题进行分形改进，即确定解在$\alpha$ -Hausdorff度量($\alpha$ -a.e.)的几乎所有地方都收敛到初始数据所需的最小正则性。我们扩展到分形设置($\alpha

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