We prove that, given~$p>\max\left\{\frac{2n}{n+2},1\right\}$, the nonnegative almost minimizers of the nonlinear free boundary functional $$ J_p(u,\Omega):=\int_{\Omega}\Big( |\nabla u(x)|^p+\chi_{\{u>0\}}(x)\Big)\,dx$$ are Lipschitz continuous.
Dipierro, S., Ferrari, F., Forcillo, N., Valdinoci, E. (2024). Lipschitz regularity of almost minimizers in one-phase problems driven by the p-Laplace operator. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 73(3), 813-854 [10.1512/iumj.2024.73.9926].
Lipschitz regularity of almost minimizers in one-phase problems driven by the p-Laplace operator
Ferrari, Fausto
;
2024
Abstract
We prove that, given~$p>\max\left\{\frac{2n}{n+2},1\right\}$, the nonnegative almost minimizers of the nonlinear free boundary functional $$ J_p(u,\Omega):=\int_{\Omega}\Big( |\nabla u(x)|^p+\chi_{\{u>0\}}(x)\Big)\,dx$$ are Lipschitz continuous.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
2206.03238v1 (5).pdf
accesso aperto
Tipo:
Postprint
Licenza:
Licenza per Accesso Aperto. Creative Commons Attribuzione (CCBY)
Dimensione
381.36 kB
Formato
Adobe PDF
|
381.36 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
