Global $L^\infty$-estimate for general quasilinear elliptic equations in arbitrary domains of $\mathbb{R}^N$
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929337387712512 |
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| author | Carl, Siegfried Tehrani, Hossein |
| author_facet | Carl, Siegfried Tehrani, Hossein |
| contents | In this paper our main goal is to present a new global $L^\infty$-estimate for a general class of quasilinear elliptic equations of the form $$ -div \mathcal{A}(x,u,\nabla u)=\mathcal{B}(x,u,\nabla u) $$ under minimal structure conditions on the functions $\mathcal{A}$ and $\mathcal{B}$, and in arbitrary domains of $\mathbb{R}^N$. The main focus and the novelty of the paper is to prove $L^\infty$-estimate of the form $$ |u|_{\infty, Ω}\le C Φ(|u|_{β,Ω}) $$ where $Φ: \mathbb{R}^+\to \mathbb{R}^+$ is a data independent function with $\lim_{s\to 0^+}Φ(s)=0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_16719 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Global $L^\infty$-estimate for general quasilinear elliptic equations in arbitrary domains of $\mathbb{R}^N$ Carl, Siegfried Tehrani, Hossein Analysis of PDEs In this paper our main goal is to present a new global $L^\infty$-estimate for a general class of quasilinear elliptic equations of the form $$ -div \mathcal{A}(x,u,\nabla u)=\mathcal{B}(x,u,\nabla u) $$ under minimal structure conditions on the functions $\mathcal{A}$ and $\mathcal{B}$, and in arbitrary domains of $\mathbb{R}^N$. The main focus and the novelty of the paper is to prove $L^\infty$-estimate of the form $$ |u|_{\infty, Ω}\le C Φ(|u|_{β,Ω}) $$ where $Φ: \mathbb{R}^+\to \mathbb{R}^+$ is a data independent function with $\lim_{s\to 0^+}Φ(s)=0$. |
| title | Global $L^\infty$-estimate for general quasilinear elliptic equations in arbitrary domains of $\mathbb{R}^N$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2310.16719 |