Qualitative properties of the fractional magnetic $p$-Laplacian and applications to critical quasilinear problems
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918375574208512 |
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| author | Baldelli, Laura Bernini, Federico |
| author_facet | Baldelli, Laura Bernini, Federico |
| contents | We investigate the fractional magnetic $p$-Laplacian operator in the physical dimension case $N=3$, with $0<s<1<p$ and $sp<3$. Our goal is twofold. First, we define and study suitable functional settings for such operator proving significant properties. Then we get the existence of weak solutions for some quasilinear equations involving a weighted critical and subcritical power type nonlinearity. Our technique relies on variational methods and faces various difficulties: the complex quasilinear framework due to the presence of an external magnetic potential, the nonlocal setting, which entails appropriate tools, and the lack of compactness, which requires concentration compactness arguments. In this direction, we state a new concentration compactness principle in the quasilinear magnetic setting that seems to be missing in the literature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_06089 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Qualitative properties of the fractional magnetic $p$-Laplacian and applications to critical quasilinear problems Baldelli, Laura Bernini, Federico Analysis of PDEs 35J62, 35Q60, 35R11, 35B33 We investigate the fractional magnetic $p$-Laplacian operator in the physical dimension case $N=3$, with $0<s<1<p$ and $sp<3$. Our goal is twofold. First, we define and study suitable functional settings for such operator proving significant properties. Then we get the existence of weak solutions for some quasilinear equations involving a weighted critical and subcritical power type nonlinearity. Our technique relies on variational methods and faces various difficulties: the complex quasilinear framework due to the presence of an external magnetic potential, the nonlocal setting, which entails appropriate tools, and the lack of compactness, which requires concentration compactness arguments. In this direction, we state a new concentration compactness principle in the quasilinear magnetic setting that seems to be missing in the literature. |
| title | Qualitative properties of the fractional magnetic $p$-Laplacian and applications to critical quasilinear problems |
| topic | Analysis of PDEs 35J62, 35Q60, 35R11, 35B33 |
| url | https://arxiv.org/abs/2603.06089 |