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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.07728 |
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| _version_ | 1866914848335462400 |
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| author | Fischer, Florian |
| author_facet | Fischer, Florian |
| contents | We construct optimal Hardy weights to subcritical energy functionals $h$ associated with quasilinear Schrödinger operators on locally finite graphs. Here, optimality means that the weight $w$ is the largest possible with respect to a partial ordering, and that the corresponding shifted energy functional $h-w$ is null-critical. Moreover, we show a decay condition of Hardy weights in terms of their integrability with respect to certain integral weights. As an application of the decay condition, we show that null-criticality implies optimality near infinity. We also briefly discuss an uncertainty-type principle and a Rellich-type inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_07728 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Optimality and Decay of $p$-Hardy Weights on Graphs Fischer, Florian Analysis of PDEs Mathematical Physics Functional Analysis 39A12 (Primary), 31C20, 31C45, 35R02 (Secondary) We construct optimal Hardy weights to subcritical energy functionals $h$ associated with quasilinear Schrödinger operators on locally finite graphs. Here, optimality means that the weight $w$ is the largest possible with respect to a partial ordering, and that the corresponding shifted energy functional $h-w$ is null-critical. Moreover, we show a decay condition of Hardy weights in terms of their integrability with respect to certain integral weights. As an application of the decay condition, we show that null-criticality implies optimality near infinity. We also briefly discuss an uncertainty-type principle and a Rellich-type inequality. |
| title | On the Optimality and Decay of $p$-Hardy Weights on Graphs |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis 39A12 (Primary), 31C20, 31C45, 35R02 (Secondary) |
| url | https://arxiv.org/abs/2212.07728 |