Almost minimizers for certain fractional variational problems

Seongmin Jeon; Arshak Petrosyan

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arXiv · 1905.11961

Almost minimizers for certain fractional variational problems

Seongmin Jeon·Arshak Petrosyan

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Abstract

In this paper we introduce a notion of almost minimizers for certain variational problems governed by the fractional Laplacian, with the help of the Caffarelli-Silvestre extension. In particular, we study almost fractional harmonic functions and almost minimizers for the fractional obstacle problem with zero obstacle. We show that for a certain range of parameters, almost minimizers are almost Lipschitz or $C^{1,\beta}$-regular.

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Seongmin Jeon, Arshak Petrosyan. 2019-05-28. Almost minimizers for certain fractional variational problems. https://arxiv.org/abs/1905.11961

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