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MATHEMATICAL METHODS IN THE APPLIED SCIENCES Math. Meth. Appl. Sci. 2003; 26:10931136 (DOI: 10.1002/mma.402)
 

Summary: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Math. Meth. Appl. Sci. 2003; 26:1093≠1136 (DOI: 10.1002/mma.402)
MOS subject classiˇcation: 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
B√en√edicte Alziary1;
, Jacqueline Fleckinger-Pell√e1;
and Peter Tak√ańc2;;ß
1CEREMATH--UMR MIP; Universit√e des Sciences Sociales; 21 All√ees 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 Aharonov≠Bohm-type magnetic potential is investigated. It is shown that, for the ˇrst
eigenvalue 1 (the ground state energy), the following two statements are equivalent: (I) the magnetic

  

Source: Alziary-Chassat, Bťnťdicte - Universitť Toulouse 1 - Capitole

 

Collections: Mathematics