Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.01607 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- In this paper, we study superlinear systems that give rise to free boundaries. Such systems appear for example from the minimization of the energy functional $$ \int_Ω\left(|\nabla\mathbf{u}|^2+\frac2p|\mathbf{u}|^p\right),\quad 0<p<1, $$ but solutions can be also understood in an ad hoc viscosity way. First, we prove the optimal regularity of minimizers using a variational approach. Then, we apply a linearization technique to establish the $C^{1,α}$-regularity of the ``flat'' part of the free boundary via a viscosity method. Finally, for minimizing free boundaries, we extend this result to analyticity.