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A Lyapunov type inequality for indefinite weights and eigenvalue homogenization


Authors: Julián Fernández Bonder, Juan Pablo Pinasco and Ariel Martin Salort
Journal: Proc. Amer. Math. Soc. 144 (2016), 1669-1680
MSC (2010): Primary 35P15, 35B27; Secondary 35P30
DOI: https://doi.org/10.1090/proc/12871
Published electronically: September 15, 2015
MathSciNet review: 3451242
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Abstract: In this paper we prove a Lyapunov type inequality for quasilinear problems with indefinite weights. We show that the first eigenvalue is bounded below in terms of the integral of the weight, instead of the integral of its positive part. We apply this inequality to some eigenvalue homogenization problems with indefinite weights.


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Additional Information

Julián Fernández Bonder
Affiliation: Departamento de Matemática and IMAS - CONICET, FCEyN - Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I (1428) Av. Cantilo s/n. Buenos Aires, Argentina
Email: jfbonder@dm.uba.ar

Juan Pablo Pinasco
Affiliation: Departamento de Matemática and IMAS - CONICET, FCEyN - Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I (1428) Av. Cantilo s/n. Buenos Aires, Argentina.
Email: jpinasco@dm.uba.ar

Ariel Martin Salort
Affiliation: Departamento de Matemática and IMAS - CONICET, FCEyN - Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I (1428) Av. Cantilo s/n. Buenos Aires, Argentina
Email: asalort@dm.uba.ar

DOI: https://doi.org/10.1090/proc/12871
Keywords: Lyapunov's inequality, eigenvalues, $p$-Laplacian, homogenization
Received by editor(s): December 27, 2014
Received by editor(s) in revised form: May 6, 2015
Published electronically: September 15, 2015
Additional Notes: The authors are members of CONICET (Argentina). This work was partially supported by Universidad de Buenos Aires under grant 20020130100283BA, and ANPCyT PICT2012 0153.
Communicated by: Catherine Sulem
Article copyright: © Copyright 2015 American Mathematical Society

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