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research article

On the Hölder regularity for the fractional Schrödinger equation and its improvement for radial data

Lemm, Marius  
November 1, 2016
Communications in Partial Differential Equations

We consider the linear, time-independent fractional Schrödinger equation. We are interested in the local Hölder exponents of distributional solutions ψ, assuming local L p integrability of the functions V and f. By standard arguments, we obtain the formula 2 s− N∕ p for the local Hölder exponent of ψ where we take some extra care regarding endpoint cases. For our main result, we assume that V and f (but not necessarily ψ) are radial functions, a situation which is commonplace in applications. We find that the regularity theory “becomes one dimensional” in the sense that the Hölder exponent improves from 2 s− N∕ p to 2 s− 1∕ p away from the origin. Similar results hold for∇ ψ as well.

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Type
research article
DOI
10.1080/03605302.2016.1227338
Author(s)
Lemm, Marius  
Date Issued

2016-11-01

Published in
Communications in Partial Differential Equations
Volume

41

Issue

11

Start page

1761

End page

1792

Editorial or Peer reviewed

REVIEWED

Written at

OTHER

EPFL units
CAMP  
Available on Infoscience
October 1, 2020
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/172099
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