6533b827fe1ef96bd128660b
RESEARCH PRODUCT
A Viscosity Equation for Minimizers of a Class of Very Degenerate Elliptic Functionals
Giulio Ciraolosubject
Viscosity solutions minimizer of convex functionals very degenerate elliptic functionalsClass (set theory)Pure mathematicsSettore MAT/05 - Analisi MatematicaBounded functionMathematical analysisDomain (ring theory)Degenerate energy levelsNabla symbolViscosity solutionConvex functionMathematicsdescription
We consider the functional $$J(v) = \int_\varOmega\bigl[f\bigl(|\nabla v|\bigr) - v\bigr] dx, $$ where Ω is a bounded domain and f:[0,+∞)→ℝ is a convex function vanishing for s∈[0,σ], with σ>0. We prove that a minimizer u of J satisfies an equation of the form $$\min\bigl(F\bigl(\nabla u, D^2 u\bigr), |\nabla u|-\sigma\bigr)=0 $$ in the viscosity sense.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-01-01 |