Positive Criticality and Optimal Hardy Inequality for Fractional Laplacians
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910235078164480 |
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| author | Hake, Philipp Keller, Matthias Pogorzelski, Felix |
| author_facet | Hake, Philipp Keller, Matthias Pogorzelski, Felix |
| contents | We characterize positive critical Hardy weights for general Laplacians on weighted graphs. We then apply this result to fractional Laplacians on general graphs and use the characterization to identify an optimal Hardy weight under suitable assumptions. We finally illustrate our results with examples of graphs which arise as Cayley graphs of groups, satisfy curvature assumptions or are fractal graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19423 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Positive Criticality and Optimal Hardy Inequality for Fractional Laplacians Hake, Philipp Keller, Matthias Pogorzelski, Felix Mathematical Physics Analysis of PDEs Spectral Theory We characterize positive critical Hardy weights for general Laplacians on weighted graphs. We then apply this result to fractional Laplacians on general graphs and use the characterization to identify an optimal Hardy weight under suitable assumptions. We finally illustrate our results with examples of graphs which arise as Cayley graphs of groups, satisfy curvature assumptions or are fractal graphs. |
| title | Positive Criticality and Optimal Hardy Inequality for Fractional Laplacians |
| topic | Mathematical Physics Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2605.19423 |