Limits at infinity for Hajłasz-Sobolev functions in metric spaces
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_ | 1866908394964647936 |
|---|---|
| author | Agarwal, Angha Vähäkangas, Antti V. |
| author_facet | Agarwal, Angha Vähäkangas, Antti V. |
| contents | We study limits at infinity for homogeneous Hajlasz-Sobolev functions defined on uniformly perfect metric spaces equipped with a doubling measure. We prove that a quasicontinuous representative of such a function has a pointwise limit at infinity outside an exceptional set, defined in terms of a variational relative capacity. Our framework refines earlier approaches that relied on Hausdorff content rather than relative capacity, and it extends previous results for homogeneous Newtonian and fractional Sobolev functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05037 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limits at infinity for Hajłasz-Sobolev functions in metric spaces Agarwal, Angha Vähäkangas, Antti V. Classical Analysis and ODEs Analysis of PDEs 46E36, 31C15, 31B15, 31B25 We study limits at infinity for homogeneous Hajlasz-Sobolev functions defined on uniformly perfect metric spaces equipped with a doubling measure. We prove that a quasicontinuous representative of such a function has a pointwise limit at infinity outside an exceptional set, defined in terms of a variational relative capacity. Our framework refines earlier approaches that relied on Hausdorff content rather than relative capacity, and it extends previous results for homogeneous Newtonian and fractional Sobolev functions. |
| title | Limits at infinity for Hajłasz-Sobolev functions in metric spaces |
| topic | Classical Analysis and ODEs Analysis of PDEs 46E36, 31C15, 31B15, 31B25 |
| url | https://arxiv.org/abs/2506.05037 |