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arxiv: 1506.05325 · v1 · pith:6OAGETJPnew · submitted 2015-06-17 · 🧮 math.CA · math.AP

An improved necessary condition for the Schr\"odinger maximal estimate

Renato Luc\`a , Keith Rogers This is my paper
classification 🧮 math.CA math.AP
keywords conditionnecessaryodingerschralmostcarlesonconvergenceconverges
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We improve the necessary condition for Carleson's problem regarding convergence for the Schr\"odinger equation in dimensions $n\ge 3$. We prove that if the solution converges almost everywhere to its initial datum as time tends to zero, for all data in $H^s(\mathbb{R}^n)$, then $s\ge \frac{n}{2(n+2)}$.

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