mirror coupling
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2021 ◽  
Vol 111 (1) ◽  
Author(s):  
Oliver Fürst ◽  
Batu Güneysu

AbstractWe use the mirror coupling of Brownian motion to show that under a $$\beta \in (0,1)$$ β ∈ ( 0 , 1 ) -dependent Kato-type assumption on the possibly nonsmooth electromagnetic potential, the corresponding magnetic Schrödinger semigroup in $${\mathbb {R}}^d$$ R d has a global $$L^{p}$$ L p -to-$$C^{0,\beta }$$ C 0 , β Hölder smoothing property for all $$p\in [1,\infty ]$$ p ∈ [ 1 , ∞ ] ; in particular, his all eigenfunctions are uniformly $$\beta $$ β -Hölder continuous. This result shows that the eigenfunctions of the Hamilton operator of a molecule in a magnetic field are uniformly $$\beta $$ β -Hölder continuous under weak $$L^q$$ L q -assumptions on the magnetic potential.


Author(s):  
Ma Zhu ◽  
Wu Guodong ◽  
Gong Da ◽  
Jiang Qiuyue ◽  
Sun Xiang

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