Regularizing effects for an elliptic system of singular equations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911079024558080 |
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| author | Giannone, Gabriele |
| author_facet | Giannone, Gabriele |
| contents | A system of two singular semi-linear elliptic equations, patterned after the Schrödinger-Maxwell system, is considered. If the reaction term of the first equation contains a datum $f\in L^m$, existence of positive solutions with finite energy is established for suitable ranges of $m$. In particular, the results from the theory of elliptic single equations are improved. At the same time, thanks to an approach based on approximation schemes and a priori estimates on the approximated sequences of solutions, it is shown that the integrability assumptions on the datum produce higher integrability of the solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19177 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularizing effects for an elliptic system of singular equations Giannone, Gabriele Analysis of PDEs 35J75, 35B45 (Primary) 35J57, 35B09 (Secondary) A system of two singular semi-linear elliptic equations, patterned after the Schrödinger-Maxwell system, is considered. If the reaction term of the first equation contains a datum $f\in L^m$, existence of positive solutions with finite energy is established for suitable ranges of $m$. In particular, the results from the theory of elliptic single equations are improved. At the same time, thanks to an approach based on approximation schemes and a priori estimates on the approximated sequences of solutions, it is shown that the integrability assumptions on the datum produce higher integrability of the solutions. |
| title | Regularizing effects for an elliptic system of singular equations |
| topic | Analysis of PDEs 35J75, 35B45 (Primary) 35J57, 35B09 (Secondary) |
| url | https://arxiv.org/abs/2505.19177 |