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.
Data di pubblicazione: | 2013 |
Titolo: | A viscosity equation for minimizers of a class of very degenerate elliptic functionals. |
Autori: | |
Citazione: | 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. |
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. |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/978-88-470-2841-8_5 |
URL: | http://www.springer.com/mathematics/analysis/book/978-88-470-2840-1?changeHeader |
Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica |
Appare nelle tipologie: | 2.01 Capitolo o Saggio |
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