Asymptotics as $s\searrow 0$ of the nonlocal nonparametric Plateau problem with obstacles

Claudia Bucur; Luca Lombardini

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arXiv · 2604.11520

Asymptotics as $s\searrow 0$ of the nonlocal nonparametric Plateau problem with obstacles

Claudia Bucur·Luca Lombardini

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Abstract

In this paper, we introduce a functional and a geometric setting for an obstacle problem for nonlocal minimal graphs. In particular we study existence of solutions, a priori estimates, and we prove the equivalence of the two settings. We then observe a striking stickiness phenomena when the fractional parameter is small and the data at infinity is not too large: the nonlocal minimal graphs adhere entirely to the obstacle and leave the remainder of the domain asymptotically empty. We thus provide a class of examples where continuity of nonlocal minimal graphs across the boundary and across the obstacle may fail.

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Claudia Bucur, Luca Lombardini. 2026-04-13. Asymptotics as $s\searrow 0$ of the nonlocal nonparametric Plateau problem with obstacles. https://arxiv.org/abs/2604.11520

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