Answers are grounded in this paper and cite their sources.
We consider the PDEs version of the Carleson problem in the context of the cubic nonlinear Klein-Gordon equation. This means that we aim to establish the lowest regularity class for which one has almost everywhere pointwise convergence of the solutions to the initial data, as t → 0. We prove sharp results for initial data in Sobolev spaces and for their randomized counterparts.
No takes yet. Share an insight, caveat, or question.
Lucà et al. (2024) studied this question.
Synapse has enriched 8 closely related papers on similar clinical questions. Consider them for comparative context: