Global Lipschitz continuity for minima of degenerate problems

2015/04/23 by Bousquet, Pierre, Brasco, Lorenzo
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1504.06101

Abstract

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 \it only outside a ball and no growth assumptions are made.

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