Weak derivatives and metric differentiability almost everywhere
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909887028527104 |
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| author | Evseev, Nikita |
| author_facet | Evseev, Nikita |
| contents | It is known that a Lipschitz continuous map from the Euclidean domain to a metric space is metrically differentiable almost everywhere. When the metric space is a Banach space dual to separable, the metric differential has its linear counterpart -- weak* differential. However, for an arbitrary metric or Banach space, a Lipschitz map is not necessarily weak* differentiable. This paper introduces an approach based on a concept of weak weak* derivatives. This framework yields a linear representation for the metric differential, allowing for its calculation as the norm of an associated linear operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02520 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak derivatives and metric differentiability almost everywhere Evseev, Nikita Functional Analysis Metric Geometry 30Lxx, 46E36, 46B25 It is known that a Lipschitz continuous map from the Euclidean domain to a metric space is metrically differentiable almost everywhere. When the metric space is a Banach space dual to separable, the metric differential has its linear counterpart -- weak* differential. However, for an arbitrary metric or Banach space, a Lipschitz map is not necessarily weak* differentiable. This paper introduces an approach based on a concept of weak weak* derivatives. This framework yields a linear representation for the metric differential, allowing for its calculation as the norm of an associated linear operator. |
| title | Weak derivatives and metric differentiability almost everywhere |
| topic | Functional Analysis Metric Geometry 30Lxx, 46E36, 46B25 |
| url | https://arxiv.org/abs/2511.02520 |