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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2505.17289 |
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| _version_ | 1866909620917764096 |
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| author | Guevara, Diego Alexander Castro |
| author_facet | Guevara, Diego Alexander Castro |
| contents | In this paper we study the problem \[ \begin{cases} -Δ_d u = μ_0 &\text{ in } G\\ u = 0 &\text{ on } \partial G \end{cases} \] where, $Δ_d$ represent the discret Laplacian, and $μ_0$ it is a measure defined in the vertex of the graph $G=(V,E)$. Here $V$ defined the vertex of the graph, $E$ its edges and $\partial G$ its boundary. We prove that this problem has an unique solution by using an adaption of the Perron's method for the graphs by using an idea known as Balayage. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17289 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Poisson's Problems on graphs Guevara, Diego Alexander Castro Analysis of PDEs In this paper we study the problem \[ \begin{cases} -Δ_d u = μ_0 &\text{ in } G\\ u = 0 &\text{ on } \partial G \end{cases} \] where, $Δ_d$ represent the discret Laplacian, and $μ_0$ it is a measure defined in the vertex of the graph $G=(V,E)$. Here $V$ defined the vertex of the graph, $E$ its edges and $\partial G$ its boundary. We prove that this problem has an unique solution by using an adaption of the Perron's method for the graphs by using an idea known as Balayage. |
| title | The Poisson's Problems on graphs |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.17289 |