Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.14565 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916250861436928 |
|---|---|
| author | Gobbino, Massimo Picenni, Nicola |
| author_facet | Gobbino, Massimo Picenni, Nicola |
| contents | We investigate the asymptotic behavior of minimizers for the singularly perturbed Perona-Malik functional in one dimension. In a previous study, we have shown that blow-ups of these minimizers at a suitable scale converge to staircase-like piecewise constant functions.
Building upon these findings, we delve into finer scales, revealing that both the vertical and horizontal regions of the staircase steps display cubic polynomial behavior after appropriate rescaling.
Our analysis hinges on identifying the dominant terms of the functional within each regime, elucidating the mechanisms driving the observed asymptotic behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_14565 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multi-scale analysis of minimizers for a second order regularization of the Perona-Malik functional Gobbino, Massimo Picenni, Nicola Analysis of PDEs Functional Analysis Optimization and Control 49J45, 35B25 We investigate the asymptotic behavior of minimizers for the singularly perturbed Perona-Malik functional in one dimension. In a previous study, we have shown that blow-ups of these minimizers at a suitable scale converge to staircase-like piecewise constant functions. Building upon these findings, we delve into finer scales, revealing that both the vertical and horizontal regions of the staircase steps display cubic polynomial behavior after appropriate rescaling. Our analysis hinges on identifying the dominant terms of the functional within each regime, elucidating the mechanisms driving the observed asymptotic behavior. |
| title | Multi-scale analysis of minimizers for a second order regularization of the Perona-Malik functional |
| topic | Analysis of PDEs Functional Analysis Optimization and Control 49J45, 35B25 |
| url | https://arxiv.org/abs/2311.14565 |