Global Lipschitz continuity for minima of degenerate problems

Pierre Bousquet (1) , Lorenzo Brasco (2, 3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 DMCS - Dipartimento di Matematica e Informatica = Department of Mathematics and Computer Science [Ferrara]
3 I2M - Institut de Mathématiques de Marseille

We 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.

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Pierre Bousquet, Lorenzo Brasco. Global Lipschitz continuity for minima of degenerate problems. Mathematische Annalen, 2016, ⟨10.1007/s00208-016-1362-9⟩. ⟨hal-01144517⟩