On the Pointwise Convergence of Solutions to the Schrödinger Equation Along Certain Highly Tangential Curves
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911592301461504 |
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| author | Minguillón, Javier Soria, Fernando Vargas, Ana |
| author_facet | Minguillón, Javier Soria, Fernando Vargas, Ana |
| contents | We investigate the Sobolev regularity required for almost everywhere convergence to the initial datum of solutions to the linear Schrödinger equation along certain tangential curves. In the regime $α<\tfrac12$, we analyze maximal estimates for expressions of the form $e^{itΔ}f(x+γ(t))$ over specific $α$-Hölder curves $γ$ and initial data $f\in H^s(\mathbb{R}^n)$. For the model family $γ(t)=(t^{α_1},\ldots,t^{α_n})$, where $α=\min_j α_j$, we show that the critical regularity is $s=\max\left\{\frac{1-2α}{2},\frac{n}{2(n+1)}\right\}.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12795 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Pointwise Convergence of Solutions to the Schrödinger Equation Along Certain Highly Tangential Curves Minguillón, Javier Soria, Fernando Vargas, Ana Classical Analysis and ODEs Analysis of PDEs We investigate the Sobolev regularity required for almost everywhere convergence to the initial datum of solutions to the linear Schrödinger equation along certain tangential curves. In the regime $α<\tfrac12$, we analyze maximal estimates for expressions of the form $e^{itΔ}f(x+γ(t))$ over specific $α$-Hölder curves $γ$ and initial data $f\in H^s(\mathbb{R}^n)$. For the model family $γ(t)=(t^{α_1},\ldots,t^{α_n})$, where $α=\min_j α_j$, we show that the critical regularity is $s=\max\left\{\frac{1-2α}{2},\frac{n}{2(n+1)}\right\}.$ |
| title | On the Pointwise Convergence of Solutions to the Schrödinger Equation Along Certain Highly Tangential Curves |
| topic | Classical Analysis and ODEs Analysis of PDEs |
| url | https://arxiv.org/abs/2604.12795 |