تقرير
The space of Hardy-weights for quasilinear operators on discrete graphs
| العنوان: | The space of Hardy-weights for quasilinear operators on discrete graphs |
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| المؤلفون: | Das, Ujjal, Keller, Matthias, Pinchover, Yehuda |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematical Physics, Mathematics - Classical Analysis and ODEs, Mathematics - Functional Analysis, Mathematics - Spectral Theory, 39A12, 35R02, 49J40, 31C20, 35J62 |
| الوصف: | We study Hardy inequalities for $p$-Schr\"odinger operators on general weighted graphs. Specifically, we prove a Maz'ya-type result, where we characterize the space of Hardy weights for $ p $-Schr\"odinger operators via a generalized capacity. The novel ingredient in the proof is the demonstration that the simplified energy of the $ p $-Schr\"odinger 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. Comment: 24 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.02116 |
| رقم الأكسشن: | edsarx.2407.02116 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |