A-priori bounds for a quasilinear problem in critical dimension
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866916854304342016 |
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| author | Romani, Giulio |
| author_facet | Romani, Giulio |
| contents | We establish uniform a-priori bounds for solutions of the quasilinear problem $-Δ_Nu=f(u)$ in $Ω$, with $u=0$ on $\partialΩ$, where $Ω\subset\mathbb{R}^N$ is a bounded smooth and convex domain, and $f$ is a positive superlinear and subcritical function in the sense of the Trudinger-Moser inequality. The typical growth of $f$ is thus exponential. Finally, a generalization of the result for nonhomogeneous nonlinearities is given. Using a blow-up approach, this paper completes the results in [Damascelli-Pardo, Nonlinear Anal. Real World Appl. 41 (2018)] and [Lorca-Ruf-Ubilla, J. Differential Equations 246 no. 5 (2009)], enlarging the class of nonlinearities for which the uniform a-priori bound applies. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1802_05777 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | A-priori bounds for a quasilinear problem in critical dimension Romani, Giulio Analysis of PDEs 35J92, 35B45, 35B44 We establish uniform a-priori bounds for solutions of the quasilinear problem $-Δ_Nu=f(u)$ in $Ω$, with $u=0$ on $\partialΩ$, where $Ω\subset\mathbb{R}^N$ is a bounded smooth and convex domain, and $f$ is a positive superlinear and subcritical function in the sense of the Trudinger-Moser inequality. The typical growth of $f$ is thus exponential. Finally, a generalization of the result for nonhomogeneous nonlinearities is given. Using a blow-up approach, this paper completes the results in [Damascelli-Pardo, Nonlinear Anal. Real World Appl. 41 (2018)] and [Lorca-Ruf-Ubilla, J. Differential Equations 246 no. 5 (2009)], enlarging the class of nonlinearities for which the uniform a-priori bound applies. |
| title | A-priori bounds for a quasilinear problem in critical dimension |
| topic | Analysis of PDEs 35J92, 35B45, 35B44 |
| url | https://arxiv.org/abs/1802.05777 |