Non-bilinear Dirichlet Functionals: Markovianity, locality, invariance
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911190800662528 |
|---|---|
| author | Brigati, Giovanni Schiavo, Lorenzo Dello |
| author_facet | Brigati, Giovanni Schiavo, Lorenzo Dello |
| contents | We present in a unified setting the foundations for a theory of non-bilinear Dirichlet functionals on Hilbert spaces. We prove known and new equivalences between non-linear semigroups, non-linear resolvents, non-linear generators, and their energy functionals, including a complete characterization of Markovianity. We introduce and characterize strong notions of invariance for general lower semicontinuous convex functionals, and notions of locality and strong locality for non-bilinear Dirichlet functionals. Contrary to many partial results in the literature, these characterizations are complete and correctly extend the analogous assertions for the bilinear case in full generality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02942 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-bilinear Dirichlet Functionals: Markovianity, locality, invariance Brigati, Giovanni Schiavo, Lorenzo Dello Functional Analysis Probability 47H05, 47H20 (Primary) 31C25, 47D07, 60J46, 31C45 (Secondary) We present in a unified setting the foundations for a theory of non-bilinear Dirichlet functionals on Hilbert spaces. We prove known and new equivalences between non-linear semigroups, non-linear resolvents, non-linear generators, and their energy functionals, including a complete characterization of Markovianity. We introduce and characterize strong notions of invariance for general lower semicontinuous convex functionals, and notions of locality and strong locality for non-bilinear Dirichlet functionals. Contrary to many partial results in the literature, these characterizations are complete and correctly extend the analogous assertions for the bilinear case in full generality. |
| title | Non-bilinear Dirichlet Functionals: Markovianity, locality, invariance |
| topic | Functional Analysis Probability 47H05, 47H20 (Primary) 31C25, 47D07, 60J46, 31C45 (Secondary) |
| url | https://arxiv.org/abs/2510.02942 |