Limit as $p(x)\rightarrow \infty$ of $p(x)$-Harmonic functions for unbounded $p(x)$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917415731855360 |
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| author | Rouhani, Behzad Djafari Lang, Jan Méndez, Osvaldo |
| author_facet | Rouhani, Behzad Djafari Lang, Jan Méndez, Osvaldo |
| contents | It is shown that if $p_n$ is a sequence of continuous, unbounded exponents on a bounded, smooth domain $Ω\subset {\mathbb R}^n$ with $1<\inf\limits_{x\in Ω}p_n(x)$ and $p_n\rightarrow \infty$ uniformly, then the sequence $(u_n)$ of solutions of the $p_n(\cdot)$-Laplacian converges to the viscosity solution of a suitable differential operator. The novelty here is that each term of the sequence of exponents $(p_n)$ is allowed to be unbounded in $Ω$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15523 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Limit as $p(x)\rightarrow \infty$ of $p(x)$-Harmonic functions for unbounded $p(x)$ Rouhani, Behzad Djafari Lang, Jan Méndez, Osvaldo Analysis of PDEs Functional Analysis It is shown that if $p_n$ is a sequence of continuous, unbounded exponents on a bounded, smooth domain $Ω\subset {\mathbb R}^n$ with $1<\inf\limits_{x\in Ω}p_n(x)$ and $p_n\rightarrow \infty$ uniformly, then the sequence $(u_n)$ of solutions of the $p_n(\cdot)$-Laplacian converges to the viscosity solution of a suitable differential operator. The novelty here is that each term of the sequence of exponents $(p_n)$ is allowed to be unbounded in $Ω$. |
| title | Limit as $p(x)\rightarrow \infty$ of $p(x)$-Harmonic functions for unbounded $p(x)$ |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2604.15523 |