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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.06442 |
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| _version_ | 1866914501144608768 |
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| author | Greco, Damiano |
| author_facet | Greco, Damiano |
| contents | We prove Brezis--Browder type results for fractional Sobolev spaces and quantitative type estimates for $s$-harmonic functions. Furthermore, we give sufficient conditions for distributional solutions to the fractional Poisson's equation $(-Δ)^su=T$ on $\mathbb{R}^d$ to be of the form $$u(x)=\int_{\mathbb{R}^d}\frac{T(y)}{|x-y|^{d-2s}}dy+l,\quad l\in \mathbb{R}.$$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06442 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Elementary Brezis-Browder type results and Representation formulae for s-harmonic functions Greco, Damiano Analysis of PDEs Primary 35R11, 42B37 We prove Brezis--Browder type results for fractional Sobolev spaces and quantitative type estimates for $s$-harmonic functions. Furthermore, we give sufficient conditions for distributional solutions to the fractional Poisson's equation $(-Δ)^su=T$ on $\mathbb{R}^d$ to be of the form $$u(x)=\int_{\mathbb{R}^d}\frac{T(y)}{|x-y|^{d-2s}}dy+l,\quad l\in \mathbb{R}.$$ |
| title | Elementary Brezis-Browder type results and Representation formulae for s-harmonic functions |
| topic | Analysis of PDEs Primary 35R11, 42B37 |
| url | https://arxiv.org/abs/2407.06442 |