| Autor: |
Soave, Nicola, Tortone, Giorgio |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Archive for Rational Mechanics and Analysis, 2024 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1007/s00205-024-01970-4 |
| Popis: |
We investigate the structure of the nodal set of solutions to an unstable Alt-Phillips type problem \[ -\Delta u = \lambda_+(u^+)^{p-1}-\lambda_-(u^-)^{q-1} \] where $1 \le p0$, $\lambda_- \ge 0$. The equation is characterized by the sublinear inhomogeneous character of the right hand-side, which makes difficult to adapt in a standard way classical tools from free-boundary problems, such as monotonicity formulas and blow-up arguments. Our main results are: the local behavior of solutions close to the nodal set; the complete classification of the admissible vanishing orders, and estimates on the Hausdorff dimension of the singular set, for local minimizers; the existence of degenerate (not locally minimal) solutions. |
| Databáze: |
arXiv |
| Externí odkaz: |
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