Convergence over fractals for the Schrödinger equation
Year: 2021
Type: preprint
Abstract: We consider a fractal refinement of the Carleson problem for the Schrödinger 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 $α$-Hausdorff measure ($α$-a.e.). We extend to the fractal setting ($α< n$) a recent counterexample of Bourgain \cite{Bourgain2016}, which is sharp in the Lebesque measure setting ($α= n$). In doing so we recover the necessary condition from \cite{zbMATH07036806} for pointwise convergence~$α$-a.e. and we extend it to the range $n/2
Source: arXiv (Cornell University)
Authors: Lucà, Renato, Ponce-Vanegas, Felipe
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Eusko Jaurlaritza
OpenAlex ID: W3120569918