Sharp Regularity Theory for Critical Quasilinear Degenerate Parabolic Systems
Fuente:
Zenodo
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Recurso digital |
| Veröffentlicht: |
Zenodo
2025
|
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866901777125736448 |
|---|---|
| author | SÉRGIO DE ANDRADE, PAULO |
| author_facet | SÉRGIO DE ANDRADE, PAULO |
| contents | This paper establishes a sharp regularity theory for weak solutions to a class of critical quasilinear degenerate parabolic systems. The systems are characterized by a p-Laplacian type degeneracy in the principal part and nonlinearities with critical growth in the gradient. We address the fundamental question of the Hölder continuity of the spatial gradient of weak solutions. The main difficulty arises from the interplay between the degeneracy of the diffusion operator and the critical structure of the lower-order terms, which lies at the borderline of established regularity theories. Our approach combines the method of intrinsic scaling, pioneered by DiBenedetto for scalar equations, with refined comparison arguments and a new iteration scheme tailored to the systemic and critical nature of the problem. We prove that weak solutions possess a locally Hölder continuous spatial gradient, and we provide an explicit estimate for the Hölder exponent based on the structural parameters of the system. This result extends the classical regularity theory to a critical setting for systems where previous methods were not applicable and provides a precise characterization of the solution's local behavior. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17690586 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Sharp Regularity Theory for Critical Quasilinear Degenerate Parabolic Systems SÉRGIO DE ANDRADE, PAULO This paper establishes a sharp regularity theory for weak solutions to a class of critical quasilinear degenerate parabolic systems. The systems are characterized by a p-Laplacian type degeneracy in the principal part and nonlinearities with critical growth in the gradient. We address the fundamental question of the Hölder continuity of the spatial gradient of weak solutions. The main difficulty arises from the interplay between the degeneracy of the diffusion operator and the critical structure of the lower-order terms, which lies at the borderline of established regularity theories. Our approach combines the method of intrinsic scaling, pioneered by DiBenedetto for scalar equations, with refined comparison arguments and a new iteration scheme tailored to the systemic and critical nature of the problem. We prove that weak solutions possess a locally Hölder continuous spatial gradient, and we provide an explicit estimate for the Hölder exponent based on the structural parameters of the system. This result extends the classical regularity theory to a critical setting for systems where previous methods were not applicable and provides a precise characterization of the solution's local behavior. |
| title | Sharp Regularity Theory for Critical Quasilinear Degenerate Parabolic Systems |
| url | https://doi.org/10.5281/zenodo.17690586 |