Hölder estimates for magnetic Schrödinger semigroups in $${\mathbb {R}}^{d}$$ from mirror coupling

• Published in: Letters in mathematical physics Vol. 111; no. 1
• Main Authors: Fürst, Oliver, Güneysu, Batu
• Format: Journal Article
• Language: English
• Published: 01.02.2021
• ISSN: 0377-9017; 1573-0530
• DOI: 10.1007/s11005-021-01360-x

Abstract We 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.