Search results for "Convex functionals"
showing 2 items of 2 documents
On Γ-convergence of pairs of dual functionals
2011
Abstract The paper considers a slightly modified notion of the Γ-convergence of convex functionals in uniformly convex Banach spaces and establishes that under standard coercitivity and growth conditions the Γ-convergence of a sequence of functionals { F j } to F ˜ implies that the corresponding sequence of dual functionals { F j ⁎ } converges in an analogous sense to the dual to F ˜ functional F ˜ ⁎ .
A Viscosity Equation for Minimizers of a Class of Very Degenerate Elliptic Functionals
2013
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.