The space of Hardy-weights for quasilinear operators on discrete graphs
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914855778254848 |
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| author | Das, Ujjal Keller, Matthias Pinchover, Yehuda |
| author_facet | Das, Ujjal Keller, Matthias Pinchover, Yehuda |
| contents | We study Hardy inequalities for $p$-Schrödinger operators on general weighted graphs. Specifically, we prove a Maz'ya-type result, where we characterize the space of Hardy weights for $ p $-Schrödinger operators via a generalized capacity. The novel ingredient in the proof is the demonstration that the simplified energy of the $ p $-Schrödinger energy functional is compatible with certain normal contractions. As a consequence, we obtain a necessary integrability criterion for Hardy weights. Finally, using some tools of criticality theory, we investigate the existence of minimizers in the Hardy inequalities and discuss relations to Cheeger type estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02116 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The space of Hardy-weights for quasilinear operators on discrete graphs Das, Ujjal Keller, Matthias Pinchover, Yehuda Analysis of PDEs Mathematical Physics Classical Analysis and ODEs Functional Analysis Spectral Theory 39A12, 35R02, 49J40, 31C20, 35J62 We study Hardy inequalities for $p$-Schrödinger operators on general weighted graphs. Specifically, we prove a Maz'ya-type result, where we characterize the space of Hardy weights for $ p $-Schrödinger operators via a generalized capacity. The novel ingredient in the proof is the demonstration that the simplified energy of the $ p $-Schrödinger energy functional is compatible with certain normal contractions. As a consequence, we obtain a necessary integrability criterion for Hardy weights. Finally, using some tools of criticality theory, we investigate the existence of minimizers in the Hardy inequalities and discuss relations to Cheeger type estimates. |
| title | The space of Hardy-weights for quasilinear operators on discrete graphs |
| topic | Analysis of PDEs Mathematical Physics Classical Analysis and ODEs Functional Analysis Spectral Theory 39A12, 35R02, 49J40, 31C20, 35J62 |
| url | https://arxiv.org/abs/2407.02116 |