We consider the problem of minimizing the Lagrangian ∫[F(∇u)+fu] among functions on Ω ⊂ RN 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.
Global Lipschitz continuity for minima of degenerate problems
BRASCO, Lorenzo
2016
Abstract
We consider the problem of minimizing the Lagrangian ∫[F(∇u)+fu] among functions on Ω ⊂ RN 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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
