TY - JOUR

T1 - Regularity for Eigenfunctions of Schrödinger Operators

AU - Ammann, Bernd

AU - Carvalho, Catarina

AU - Nistor, Victor

N1 - Funding Information:
Ammann’s manuscripts are available from http://www.berndammann.de/publications. Carvalho’s manuscripts are available from http://www.math.ist.utl.pt/∼ccarv. Nistor’s Manuscripts available from http://www.math.psu.edu/nistor/. Nistor was partially supported by the NSF Grants DMS-0713743, OCI-0749202, and DMS-1016556.

PY - 2012/7

Y1 - 2012/7

N2 - We prove a regularity result in weighted Sobolev (or Babuška-Kondratiev) spaces for the eigenfunctions of certain Schrödinger-type operators. Our results apply, in particular, to a non-relativistic Schrödinger operator of an N-electron atom in the fixed nucleus approximation. More precisely, let K m a(ℝ 3N, r S) be the weighted Sobolev space obtained by blowing up the set of singular points of the potential, satisfies (-Δ+V)u=λu in distribution sense, then u ∈K m a for all m∈ℤ + and all a ≤ 0. Our result extends to the case when b j and c ij are suitable bounded functions on the blown-up space. In the single-electron, multi-nuclei case, we obtain the same result for all a < 3/2.

AB - We prove a regularity result in weighted Sobolev (or Babuška-Kondratiev) spaces for the eigenfunctions of certain Schrödinger-type operators. Our results apply, in particular, to a non-relativistic Schrödinger operator of an N-electron atom in the fixed nucleus approximation. More precisely, let K m a(ℝ 3N, r S) be the weighted Sobolev space obtained by blowing up the set of singular points of the potential, satisfies (-Δ+V)u=λu in distribution sense, then u ∈K m a for all m∈ℤ + and all a ≤ 0. Our result extends to the case when b j and c ij are suitable bounded functions on the blown-up space. In the single-electron, multi-nuclei case, we obtain the same result for all a < 3/2.

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U2 - 10.1007/s11005-012-0551-z

DO - 10.1007/s11005-012-0551-z

M3 - Article

AN - SCOPUS:84862603682

VL - 101

SP - 49

EP - 84

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 1

ER -