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arXiv · 1905.05415

Optimal rearrangement problem and normalized obstacle problem in the fractional setting

Julián Fernández Bonder·Zhiwei Cheng·Hayk Mikayelyan
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Abstract

We consider an optimal rearrangement minimization problem involving the fractional Laplace operator $(-Δ)^s$, $0 0\}}, $$ which happens to be the fractional analogue of the normalized obstacle problem $Δu=χ_{\{u>0\}}$. A new section analyzing $s \to 1$ has been added.

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Julián Fernández Bonder, Zhiwei Cheng, Hayk Mikayelyan. 2019-05-21. Optimal rearrangement problem and normalized obstacle problem in the fractional setting. https://arxiv.org/abs/1905.05415

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