Summary: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Math. Meth. Appl. Sci. 2003; 26:1093­1136 (DOI: 10.1002/mma.402)
MOS subject classiÿcation: Primary 35 J 10; 35 B 05; Secondary 81 Q 10; 46 E 35
Eigenfunctions and Hardy inequalities for a magnetic
Schrodinger operator in R2
BÃenÃedicte Alziary1;
, Jacqueline Fleckinger-PellÃe1;
and Peter TakÃaÄc2;;§
1CEREMATH--UMR MIP; UniversitÃe des Sciences Sociales; 21 AllÃees de Brienne;
F-31042 Toulouse Cedex; France
2Fachbereich Mathematik; Universitat Rostock; Universitatsplatz 1; D-18055 Rostock; Germany
Communicated by W. Allegretto
SUMMARY
The zero set {zR2
: (z) = 0} of an eigenfunction of the Schrodinger operator LV = (i + A)2
+ V
on L2
(R2
) with an Aharonov­Bohm-type magnetic potential is investigated. It is shown that, for the ÿrst
eigenvalue 1 (the ground state energy), the following two statements are equivalent: (I) the magnetic

Source: Alziary-Chassat, Bénédicte - Université Toulouse 1 - Capitole

Collections: Mathematics