Global Lipschitz continuity for minima of degenerate problems

International audienceWe consider the problem of minimizing the Lagrangian [F (∇u)+f u] among functions on Ω ⊂ R N with given boundary datum ϕ. We prove Lipschitz regularity up to the boundary for solutions of this problem, provided Ω is convex and ϕ satisfies the bounded slope condition. The convex function F is required to satisfy a qualified form of uniform convexity only outside a ball and no growth assumptions are made