Lifting of fractional Sobolev mappings to noncompact covering space
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910750861164544 |
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| author | Van Schaftingen, Jean |
| author_facet | Van Schaftingen, Jean |
| contents | Given compact Riemannian manifolds $\mathcal{M}$ and $\mathcal{N}$, a Riemannian covering $π: \smash{\widetilde{\mathcal{N}}} \to \mathcal{N}$ by a noncompact covering space $\smash{\widetilde{\mathcal{N}}}$, $1 < p < \infty$ and $0 < s < 1$, the space of liftings of fractional Sobolev maps in $\smash{\dot{W}^{s, p}} (\mathcal{M}, \mathcal{N})$ is characterized when $sp > 1$ and an optimal nonlinear fractional Sobolev estimate is obtained when moreover $sp \ge \dim \mathcal{M}$. A nonlinear characterization of the sum of spaces $\smash{\dot{W}^{s, p}} (\mathcal{M}, \mathbb{R}) + \smash{\dot{W}^{1, sp}} (\mathcal{M}, \mathbb{R})$ is also provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_07663 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lifting of fractional Sobolev mappings to noncompact covering space Van Schaftingen, Jean Analysis of PDEs Classical Analysis and ODEs Functional Analysis 58D15 (Primary) 46E35 (Secondary) Given compact Riemannian manifolds $\mathcal{M}$ and $\mathcal{N}$, a Riemannian covering $π: \smash{\widetilde{\mathcal{N}}} \to \mathcal{N}$ by a noncompact covering space $\smash{\widetilde{\mathcal{N}}}$, $1 < p < \infty$ and $0 < s < 1$, the space of liftings of fractional Sobolev maps in $\smash{\dot{W}^{s, p}} (\mathcal{M}, \mathcal{N})$ is characterized when $sp > 1$ and an optimal nonlinear fractional Sobolev estimate is obtained when moreover $sp \ge \dim \mathcal{M}$. A nonlinear characterization of the sum of spaces $\smash{\dot{W}^{s, p}} (\mathcal{M}, \mathbb{R}) + \smash{\dot{W}^{1, sp}} (\mathcal{M}, \mathbb{R})$ is also provided. |
| title | Lifting of fractional Sobolev mappings to noncompact covering space |
| topic | Analysis of PDEs Classical Analysis and ODEs Functional Analysis 58D15 (Primary) 46E35 (Secondary) |
| url | https://arxiv.org/abs/2301.07663 |