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arXiv · 2402.05514

The Neumann condition for the superposition of fractional Laplacians

Serena Dipierro·Edoardo Proietti Lippi·Caterina Sportelli·Enrico Valdinoci
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Abstract

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.

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Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli, Enrico Valdinoci. 2024-02-08. The Neumann condition for the superposition of fractional Laplacians. https://doi.org/10.1051/cocv%2F2025015

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