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Mathematics > Analysis of PDEs

arXiv:2411.11272 (math)
[Submitted on 18 Nov 2024]

Title:The nonlocal Harnack inequality for antisymmetric functions: an approach via Bochner's relation and harmonic analysis

Authors:Serena Dipierro, Mateusz Kwaśnicki, Jack Thompson, Enrico Valdinoci
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Abstract:We revisit a Harnack inequality for antisymmetric functions that has been recently established for the fractional Laplacian and we extend it to more general nonlocal elliptic operators.
The new approach to deal with these problems that we propose in this paper leverages Bochner's relation, allowing one to relate a one-dimensional Fourier transform of an odd function with a three-dimensional Fourier transform of a radial function.
In this way, Harnack inequalities for odd functions, which are essentially Harnack inequalities of boundary type, are reduced to interior Harnack inequalities.
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35R11, 47G20, 35B50
Cite as: arXiv:2411.11272 [math.AP]
  (or arXiv:2411.11272v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2411.11272

Submission history

From: Jack Thompson [view email]
[v1] Mon, 18 Nov 2024 04:02:19 UTC (21 KB)
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