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.
Settore MAT/05 - Analisi Matematica
http://www.springer.com/mathematics/analysis/book/978-88-470-2840-1?changeHeader
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/64507
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