A viscosity equation for minimizers of a class of very degenerate elliptic functionals.

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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.
Lingua originaleEnglish
Titolo della pubblicazione ospiteGeometric Properties for Parabolic and Elliptic PDE's
Pagine67-83
Numero di pagine17
Stato di pubblicazionePublished - 2013

Serie di pubblicazioni

NomeSpringer INdAM Series, Vol. 2

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cita questo

Ciraolo, G. (2013). A viscosity equation for minimizers of a class of very degenerate elliptic functionals. In Geometric Properties for Parabolic and Elliptic PDE's (pagg. 67-83). (Springer INdAM Series, Vol. 2).