On the analytic smoothing effect for the Hartree equation with a short range interaction potential
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.05.067
Abstract: Abstract We consider the Cauchy problem for the Hartree equation in space dimension d ≥ 2 . We assume that the interaction potential V ( x ) is short range. More precisely, we consider the… read more here.
Keywords: interaction potential; short range; hartree equation; space ... See more keywords
On classical solutions to the Hartree equation
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DOI: 10.1016/j.jmaa.2020.123859
Abstract: Abstract This paper is concerned with positive classical solutions to the Hartree equation − Δ u = ( 1 | x | n − α ⁎ u p ) u p − 1 in R… read more here.
Keywords: equation; hartree equation; classical solutions; solutions hartree ... See more keywords
Convergence rate towards the fractional Hartree equation with singular potentials in higher Sobolev trace norms
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DOI: 10.1142/s0129055x2150029x
Abstract: In this work, we show convergence of the [Formula: see text]-particle bosonic Schrödinger equation towards the Hartree equation. Hereby, we extend the results of [I. Anapolitanos and M. Hott, A simple proof of convergence to… read more here.
Keywords: sobolev trace; phys; convergence; trace norms ... See more keywords