On a class of thin obstacle-type problems for the bi-Laplacian operator
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_ | 1866918343452131328 |
|---|---|
| author | Danielli, Donatella Gravina, Giovanni |
| author_facet | Danielli, Donatella Gravina, Giovanni |
| contents | This paper investigates the regularity of solutions and structural properties of the free boundary for a class of fourth-order elliptic problems with Neumann-type boundary conditions. The singular and degenerate elliptic operators studied naturally emerge from the extension procedure for higher-order fractional powers of the Laplacian, while the choice of non-linearity considered encompasses two-phase boundary obstacle problems as a special case. After establishing local regularity properties of solutions, Almgren- and Monneau-type monotonicity formulas are derived and utilized to carry out a blow-up analysis and prove a stratification result for the free boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11372 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a class of thin obstacle-type problems for the bi-Laplacian operator Danielli, Donatella Gravina, Giovanni Analysis of PDEs 35R35, 35J35, 35J58 This paper investigates the regularity of solutions and structural properties of the free boundary for a class of fourth-order elliptic problems with Neumann-type boundary conditions. The singular and degenerate elliptic operators studied naturally emerge from the extension procedure for higher-order fractional powers of the Laplacian, while the choice of non-linearity considered encompasses two-phase boundary obstacle problems as a special case. After establishing local regularity properties of solutions, Almgren- and Monneau-type monotonicity formulas are derived and utilized to carry out a blow-up analysis and prove a stratification result for the free boundary. |
| title | On a class of thin obstacle-type problems for the bi-Laplacian operator |
| topic | Analysis of PDEs 35R35, 35J35, 35J58 |
| url | https://arxiv.org/abs/2509.11372 |