| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 25 | |
| Number of page(s) | 45 | |
| DOI | https://doi.org/10.1051/cocv/2025015 | |
| Published online | 24 March 2025 | |
The Neumann condition for the superposition of fractional Laplacians
Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, WA 6009 Crawley, Australia
* Corresponding author: caterina.sportelli@uwa.edu.au
Received:
3
June
2024
Accepted:
28
January
2025
We present a new functional setting for Neumann conditions related to the superposition of (possibly infinitely many) fractional Laplace operators. We will introduce some bespoke functional framework and present minimization properties, existence and uniqueness results, asymptotic formulas, spectral analyses, rigidity results, integration by parts formulas, superpositions of fractional perimeters, as well as a study of the associated heat equation.
Mathematics Subject Classification: 35R11 / 35A15 / 35A01 / 60G22
Key words: fractional Laplacian / Neumann boundary conditions / superposition of operators / regularity results
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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