We consider the functional $$ J(v) = int_Omega [f(| abla v|) - v] dx, $$ where $Omega$ is a bounded domain and $f:[0,+infty) o RR$ is a convex function vanishing for $sin [0,sigma]$, with $sigma>0$. We prove that a minimizer $u$ of $J$ satisfies an equation of the form $$ min(F( abla u, D^2 u), | abla u|-sigma)=0 $$ in the viscosity sense.
Ciraolo, G. (2013). A viscosity equation for minimizers of a class of very degenerate elliptic functionals.. In R. Magnanini, S. Sakaguchi, & A. Alvino (a cura di), Geometric Properties for Parabolic and Elliptic PDE's (pp. 67-83). Springer [10.1007/978-88-470-2841-8_5].
A viscosity equation for minimizers of a class of very degenerate elliptic functionals.
CIRAOLO, Giulio
2013
Abstract
We consider the functional $$ J(v) = int_Omega [f(| abla v|) - v] dx, $$ where $Omega$ is a bounded domain and $f:[0,+infty) o RR$ is a convex function vanishing for $sin [0,sigma]$, with $sigma>0$. We prove that a minimizer $u$ of $J$ satisfies an equation of the form $$ min(F( abla u, D^2 u), | abla u|-sigma)=0 $$ in the viscosity sense.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
Ciraolo_final.pdf
Solo gestori archvio
Dimensione
105.63 kB
Formato
Adobe PDF
|
105.63 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
