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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An optimization problem for the first weighted eigenvalue problem plus a potential


Authors: Leandro M. Del Pezzo and Julián Fernández Bonder
Journal: Proc. Amer. Math. Soc. 138 (2010), 3551-3567
MSC (2000): Primary 49K20, 35P15, 35J10
Published electronically: April 16, 2010
MathSciNet review: 2661555
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Abstract: In this paper, we study the problem of minimizing the first eigenvalue of the $ p-$Laplacian plus a potential with weights when the potential and the weight are allowed to vary in the class of rearrangements of a given fixed potential $ V_0$ and weight $ g_0$. Our results generalize those obtained in earlier papers.


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Additional Information

Leandro M. Del Pezzo
Affiliation: Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria (1428), Buenos Aires, Argentina
Email: ldpezzo@dm.uba.ar

Julián Fernández Bonder
Affiliation: Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria (1428), Buenos Aires, Argentina
Email: jfbonder@dm.uba.ar

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10384-0
PII: S 0002-9939(10)10384-0
Keywords: Optimization, nonlinear eigenvalues, rearrangements
Received by editor(s): June 16, 2009
Received by editor(s) in revised form: October 30, 2009, and December 21, 2009
Published electronically: April 16, 2010
Additional Notes: The first author is a fellow of CONICET
The second author was supported by Universidad de Buenos Aires under grant X078 and by ANPCyT PICT2006–290. He is a member of CONICET
Communicated by: Chuu-Lian Terng
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.