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arXiv · 2404.07756

The limit as $s\nearrow 1$ of the fractional convex envelope

Begoña Barrios·Leandro M. Del Pezzo·Alexander Quaas·Julio D. Rossi
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Abstract

We study the behavior of the fractional convexity when the fractional parameter goes to 1. For any notion of convexity, the convex envelope of a datum prescribed on the boundary of a domain is defined as the largest possible convex function inside the domain that is below the datum on the boundary. Here we prove that the fractional convex envelope inside a strictly convex domain of a continuous and bounded exterior datum converges when $s\nearrow 1$ to the classical convex envelope of the restriction to the boundary of the exterior datum.

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Begoña Barrios, Leandro M. Del Pezzo, Alexander Quaas, Julio D. Rossi. 2024-04-11. The limit as $s\nearrow 1$ of the fractional convex envelope. https://arxiv.org/abs/2404.07756

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