Existence and regularity for a $p$-Laplacian problem in $\mathbb{R}^N$ with singular, convective, critical reaction
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| Format: | Preprint |
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2024
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| _version_ | 1866913343029116928 |
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| author | Baldelli, Laura Guarnotta, Umberto |
| author_facet | Baldelli, Laura Guarnotta, Umberto |
| contents | We prove an existence result for a $p$-Laplacian problem set in the whole Euclidean space and exhibiting a critical term perturbed by a singular, convective reaction. The approach used combines variational methods, truncation techniques, and concentration compactness arguments, together with set-valued analysis and fixed point theory. De Giorgi's technique, a priori gradient estimates, and nonlinear regularity theory are employed to get local $C^{1,α}$ regularity of solutions, as well as their pointwise decay at infinity. The result is new even in the non-singular case, also for the Laplacian. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_15959 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and regularity for a $p$-Laplacian problem in $\mathbb{R}^N$ with singular, convective, critical reaction Baldelli, Laura Guarnotta, Umberto Analysis of PDEs We prove an existence result for a $p$-Laplacian problem set in the whole Euclidean space and exhibiting a critical term perturbed by a singular, convective reaction. The approach used combines variational methods, truncation techniques, and concentration compactness arguments, together with set-valued analysis and fixed point theory. De Giorgi's technique, a priori gradient estimates, and nonlinear regularity theory are employed to get local $C^{1,α}$ regularity of solutions, as well as their pointwise decay at infinity. The result is new even in the non-singular case, also for the Laplacian. |
| title | Existence and regularity for a $p$-Laplacian problem in $\mathbb{R}^N$ with singular, convective, critical reaction |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.15959 |