Symmetrization of measures and the one-dimensional Poisson equation with Dirichlet boundary conditions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911007390040064 |
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| author | Papadimitriou, Christos |
| author_facet | Papadimitriou, Christos |
| contents | Let \(μ\) be a finite Borel measure on \((-π,π)\). Consider the one-dimensional Poisson equation \(-u''=μ\), where equality holds in the sense of distributions, with Dirichlet boundary conditions \(u(\pmπ)=0\). In this paper, we define measures that are transformations of \(μ\), we compare the convex integral means of the original solutions \(u_μ\) and the transformed ones, and we prove the uniqueness of a solution that maximizes the convex integral means. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13311 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetrization of measures and the one-dimensional Poisson equation with Dirichlet boundary conditions Papadimitriou, Christos Classical Analysis and ODEs 34B05, 34C10 Let \(μ\) be a finite Borel measure on \((-π,π)\). Consider the one-dimensional Poisson equation \(-u''=μ\), where equality holds in the sense of distributions, with Dirichlet boundary conditions \(u(\pmπ)=0\). In this paper, we define measures that are transformations of \(μ\), we compare the convex integral means of the original solutions \(u_μ\) and the transformed ones, and we prove the uniqueness of a solution that maximizes the convex integral means. |
| title | Symmetrization of measures and the one-dimensional Poisson equation with Dirichlet boundary conditions |
| topic | Classical Analysis and ODEs 34B05, 34C10 |
| url | https://arxiv.org/abs/2506.13311 |