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A probabilistic approach to the Liouville property for Schrödinger operators with an application to infinite configurations of balls
Author(s):
Rachel
Hess-Green;
Ross
G.
Pinsky
Journal:
Proc. Amer. Math. Soc.
138
(2010),
4487-4496.
MSC (2010):
Primary 60H30, 35J10
Posted:
June 10, 2010
MathSciNet review:
2680073
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Additional information
Abstract:
Consider the equation  in | (*) |
for  , where  . One says that the Liouville property holds if the only bounded solution to (*) is 0. Under a certain growth condition on  , we give a necessary and sufficient analytic condition for the Liouville property to hold. We then apply this to the case that  is the indicator function of an infinite collection of small balls.
References:
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Additional Information:
Rachel
Hess-Green
Affiliation:
Department of Mathematics, Technion–Israel Institute of Technology, Haifa, 32000, Israel
Email:
rachelg@tx.technion.ac.il
Ross
G.
Pinsky
Affiliation:
Department of Mathematics, Technion–Israel Institute of Technology, Haifa, 32000, Israel
Email:
pinsky@math.technion.ac.il
DOI:
10.1090/S0002-9939-2010-10452-5
PII:
S 0002-9939(2010)10452-5
Keywords:
Liouville property,
bounded solutions,
Schrödinger equation
Received by editor(s):
October 6, 2009
Received by editor(s) in revised form:
February 11, 2010
Posted:
June 10, 2010
Communicated by:
Richard C. Bradley
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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