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arXiv · 2410.22426

On a fractional magnetic pseudorelativistic operator: properties and applications

Federico Bernini·Pietro d'Avenia
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Abstract

We introduce a fractional magnetic pseudorelativistic operator for a general fractional order $s\in(0,1)$. First we define a suitable functional setting and we prove some fundamental properties. Then we show the behavior of the operator as $s \nearrow 1$ obtaining some results \`a la Bourgain-Brezis-Mironescu and removing the singularity from the integral definition. Finally we get existence of weak solutions for some semilinear equations involving a power type nonlinearity or a nonlocal (Choquard type) term.

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Federico Bernini, Pietro d'Avenia. 2024-10-29. On a fractional magnetic pseudorelativistic operator: properties and applications. https://arxiv.org/abs/2410.22426

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