Asymptotic analysis of higher-order perturbations of the Perona--Malik functional
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911467669815296 |
|---|---|
| author | Braides, Andrea Fonseca, Irene |
| author_facet | Braides, Andrea Fonseca, Irene |
| contents | The Gamma-limit of higher-order singular perturbations of the Perona-Malik functional is analyzed. The energies considered combine the critically scaled logarithmic term with a k-th order regularization designed to balance bulk and interfacial effects. A compactness result is obtained, and the Gamma-limit is identified as a free-discontinuity functional on SBV, given by the sum of the Dirichlet energy and a surface term proportional to the jump amplitude to the power 1/k. The surface density is characterized through a one-dimensional optimal-profile problem with homogeneous boundary conditions on derivatives up to order k-1. As a consequence, the limit of the same energies at a different scaling is determined. That scaling had been previously studied in the second-order case to address the so-called staircasing phenomenon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21938 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic analysis of higher-order perturbations of the Perona--Malik functional Braides, Andrea Fonseca, Irene Analysis of PDEs 49J45, 49J10, 49Q20, 26A45, 94A08 The Gamma-limit of higher-order singular perturbations of the Perona-Malik functional is analyzed. The energies considered combine the critically scaled logarithmic term with a k-th order regularization designed to balance bulk and interfacial effects. A compactness result is obtained, and the Gamma-limit is identified as a free-discontinuity functional on SBV, given by the sum of the Dirichlet energy and a surface term proportional to the jump amplitude to the power 1/k. The surface density is characterized through a one-dimensional optimal-profile problem with homogeneous boundary conditions on derivatives up to order k-1. As a consequence, the limit of the same energies at a different scaling is determined. That scaling had been previously studied in the second-order case to address the so-called staircasing phenomenon. |
| title | Asymptotic analysis of higher-order perturbations of the Perona--Malik functional |
| topic | Analysis of PDEs 49J45, 49J10, 49Q20, 26A45, 94A08 |
| url | https://arxiv.org/abs/2602.21938 |