Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.12548 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909582227406848 |
|---|---|
| author | Caffarelli, Luis Farah, Antonio Restrepo, Daniel |
| author_facet | Caffarelli, Luis Farah, Antonio Restrepo, Daniel |
| contents | In this paper, we establish regularity and uniqueness results for Grad-Mercier type equations that arise in the context of plasma physics. We show that solutions of this problem naturally develop a dead core, which corresponds to the set where the solutions become identically equal to their maximum. We prove uniqueness, sharp regularity, and non-degeneracy bounds for solutions under suitable assumptions on the reaction term. Of independent interest, our methods allow us to prove that the free boundaries of a broad class of semilinear equations have locally finite $H^{n-1}$ measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12548 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Grad-Mercier equation and Semilinear Free Boundary Problems Caffarelli, Luis Farah, Antonio Restrepo, Daniel Analysis of PDEs In this paper, we establish regularity and uniqueness results for Grad-Mercier type equations that arise in the context of plasma physics. We show that solutions of this problem naturally develop a dead core, which corresponds to the set where the solutions become identically equal to their maximum. We prove uniqueness, sharp regularity, and non-degeneracy bounds for solutions under suitable assumptions on the reaction term. Of independent interest, our methods allow us to prove that the free boundaries of a broad class of semilinear equations have locally finite $H^{n-1}$ measure. |
| title | On the Grad-Mercier equation and Semilinear Free Boundary Problems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.12548 |