A note on pointwise convergence for the Schrödinger equation

By Renato Lucà, Keith McKenzie Rogers. Mathematical Proceedings of the Cambridge Philosophical Society, 2017

51 citations recorded by the source corpus.

Abstract We consider Carleson's problem regarding pointwise convergence for the Schrödinger equation. Bourgain proved that there is initial data, in Hs(ℝn) with $s<\frac{n}{2(n+1)}$, for which the solution diverges on a set of nonzero Lebesgue measure. We provide a different example enabling the generalisation to fractional Hausdorff measure.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/4355d30e1735dcbd956130a845fc542a92298491

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In Applied Mathematics

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Citations in the corpus

• POINTWISE CONVERGENCE OF SCHRÖDINGER SOLUTIONS AND MULTILINEAR REFINED STRICHARTZ ESTIMATES (2018, unknown): “αn(s) ≥    n, s < n 2(n+1) (Bourgain [4]) n+ n n−1 − 2(n+1)s n−1 , n 2(n+1) ≤ s < n+1 8 (Lucà-Rogers [16]) n+ 1− 2(n+2)s n , n+1 8 ≤ s < n 4 (Lucà-Rogers [15]) n− 2s, n4 ≤ s ≤ n 2 (Žubrinić [18]).”
• Sharp L2 estimates of the Schrödinger maximal function in higher dimensions (2018, background): “The higher dimensional case has since been studied by several authors [7, 9, 29, 31, 2, 27, 30, 21, 3, 24, 11, 4, 25, 12, 13].”