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
2013-01-01
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.
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