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arXiv · 1504.06101

Global Lipschitz continuity for minima of degenerate problems

Pierre Bousquet·Lorenzo Brasco
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Abstract

We consider the problem of minimizing the Lagrangian $\int [F(\nabla u)+f\,u]$ among functions on $\Omega\subset\mathbb{R}^N$ with given boundary datum $\varphi$. We prove Lipschitz regularity up to the boundary for solutions of this problem, provided $\Omega$ is convex and $\varphi$ 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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Pierre Bousquet, Lorenzo Brasco. 2015-04-23. Global Lipschitz continuity for minima of degenerate problems. https://arxiv.org/abs/1504.06101

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