The Liouville theorem for discrete symmetric averaging operators
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866917640048476160 |
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| author | Adamowicz, Tomasz Llorente, José G. |
| author_facet | Adamowicz, Tomasz Llorente, José G. |
| contents | We introduce averaging operators on lattices $\mathbb{Z}^d$ and study the Liouville property for functions satisfying mean value properties associated to such operators. This framework encloses discrete harmonic, $p$-harmonic, $\infty$-harmonic and the so-called game $p$-harmonic functions. Our approach provides an elementary alternative proof of the Liouville Theorem for positive $p$-harmonic functions on $\mathbb{Z}^d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_12295 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Liouville theorem for discrete symmetric averaging operators Adamowicz, Tomasz Llorente, José G. Analysis of PDEs Metric Geometry Primary: 31C20, Secondary: 35B53, 31C45 We introduce averaging operators on lattices $\mathbb{Z}^d$ and study the Liouville property for functions satisfying mean value properties associated to such operators. This framework encloses discrete harmonic, $p$-harmonic, $\infty$-harmonic and the so-called game $p$-harmonic functions. Our approach provides an elementary alternative proof of the Liouville Theorem for positive $p$-harmonic functions on $\mathbb{Z}^d$. |
| title | The Liouville theorem for discrete symmetric averaging operators |
| topic | Analysis of PDEs Metric Geometry Primary: 31C20, Secondary: 35B53, 31C45 |
| url | https://arxiv.org/abs/2204.12295 |