2024/10/29 by Bernini, Federico, d'Avenia, Pietro
#35J61 #35Q60 #35S05 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2410.22426
We introduce a fractional magnetic pseudorelativistic operator for a general fractional order s∈(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 à 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.