On a fractional magnetic pseudorelativistic operator: properties and applications
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913567251365888 |
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| author | Bernini, Federico d'Avenia, Pietro |
| author_facet | Bernini, Federico d'Avenia, Pietro |
| contents | We introduce a fractional magnetic pseudorelativistic operator for a general fractional order $s\in(0,1)$. First we define a suitable functional setting and we prove some fundamental properties. Then we show the behavior of the operator as $s \nearrow 1$ obtaining some results à la Bourgain-Brezis-Mironescu and removing the singularity from the integral definition. Finally we get existence of weak solutions for some semilinear equations involving a power type nonlinearity or a nonlocal (Choquard type) term. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_22426 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a fractional magnetic pseudorelativistic operator: properties and applications Bernini, Federico d'Avenia, Pietro Analysis of PDEs 35S05, 35J61, 35Q60 We introduce a fractional magnetic pseudorelativistic operator for a general fractional order $s\in(0,1)$. First we define a suitable functional setting and we prove some fundamental properties. Then we show the behavior of the operator as $s \nearrow 1$ obtaining some results à la Bourgain-Brezis-Mironescu and removing the singularity from the integral definition. Finally we get existence of weak solutions for some semilinear equations involving a power type nonlinearity or a nonlocal (Choquard type) term. |
| title | On a fractional magnetic pseudorelativistic operator: properties and applications |
| topic | Analysis of PDEs 35S05, 35J61, 35Q60 |
| url | https://arxiv.org/abs/2410.22426 |