Almost minimizers for certain fractional variational problems

Jeon, S.; Petrosyan, A.

doi:10.1090/spmj/1667

Almost minimizers for certain fractional variational problems
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by S. Jeon and A. Petrosyan

St. Petersburg Math. J. 32 (2021), 729-751

DOI: https://doi.org/10.1090/spmj/1667

Published electronically: July 9, 2021

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Abstract:

A notion of almost minimizers is introduced for certain variational problems governed by the fractional Laplacian, with the help of the Caffarelli–Silvestre extension. In particular, almost fractional harmonic functions and almost minimizers for the fractional obstacle problem with zero obstacle are treated. It is shown that for a certain range of parameters, almost minimizers are almost Lipschitz or $C^{1,\beta }$-regular.

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