Nonlinear Stein theorem for differential forms
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866915219755761664 |
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| author | Sil, Swarnendu |
| author_facet | Sil, Swarnendu |
| contents | We prove that if $u$ is an $\mathbb{R}^{N}$-valued $W^{1,p}_{loc}$ differential $k$-form with $δ\left( a(x) \lvert du \rvert^{p-2} du \right) \in L^{(n,1)}_{loc}$ in a domain of $\mathbb{R}^{n}$ for $N \geq 1,$ $n \geq 2,$ $0 \leq k \leq n-1, $ $1 < p < \infty, $ with uniformly positive, bounded, Dini continuous scalar function $a$, then $du$ is continuous. This generalizes the classical result by Stein in the scalar case and the work of Kuusi-Mingione for the $p$-Laplacian type systems. We also discuss Hölder, BMO and VMO regularity estimates for such systems when $p \geq 2.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_00923 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Nonlinear Stein theorem for differential forms Sil, Swarnendu Analysis of PDEs We prove that if $u$ is an $\mathbb{R}^{N}$-valued $W^{1,p}_{loc}$ differential $k$-form with $δ\left( a(x) \lvert du \rvert^{p-2} du \right) \in L^{(n,1)}_{loc}$ in a domain of $\mathbb{R}^{n}$ for $N \geq 1,$ $n \geq 2,$ $0 \leq k \leq n-1, $ $1 < p < \infty, $ with uniformly positive, bounded, Dini continuous scalar function $a$, then $du$ is continuous. This generalizes the classical result by Stein in the scalar case and the work of Kuusi-Mingione for the $p$-Laplacian type systems. We also discuss Hölder, BMO and VMO regularity estimates for such systems when $p \geq 2.$ |
| title | Nonlinear Stein theorem for differential forms |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1810.00923 |