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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2502.16300 |
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| _version_ | 1866912242088280064 |
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| author | Jarrin, Oscar |
| author_facet | Jarrin, Oscar |
| contents | We consider an elliptic equation with the fractional Laplacian operator $(-Δ)^{\fracα{2}}$ in the dissipative term, a singular integral operator ${\bf A}(\cdot)$ in the nonlinear term, and an external source $f$. The key example is the stationary (time-independent) counterpart of the surface quasi-geostrophic equation.
Under suitable assumptions on $f$ and natural assumptions on ${\bf A}(\cdot)$ in the setting of Sobolev spaces, our main result examines how the fractional power $α$ propagates and optimally improves the regularity of weak $L^p$-solutions to this equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16300 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the fractional regularity for an elliptic nonlinear singular drift equation Jarrin, Oscar Analysis of PDEs We consider an elliptic equation with the fractional Laplacian operator $(-Δ)^{\fracα{2}}$ in the dissipative term, a singular integral operator ${\bf A}(\cdot)$ in the nonlinear term, and an external source $f$. The key example is the stationary (time-independent) counterpart of the surface quasi-geostrophic equation. Under suitable assumptions on $f$ and natural assumptions on ${\bf A}(\cdot)$ in the setting of Sobolev spaces, our main result examines how the fractional power $α$ propagates and optimally improves the regularity of weak $L^p$-solutions to this equation. |
| title | On the fractional regularity for an elliptic nonlinear singular drift equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.16300 |