An optimization problem for the first eigenvalue of the $p-$Laplacian plus a potential

Julián Fernández Bonder; Leandro M. Del Pezzo

doi:10.3934/cpaa.2006.5.675

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2006, Volume 5, Issue 4: 675-690. Doi: 10.3934/cpaa.2006.5.675

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An optimization problem for the first eigenvalue of the $p-$Laplacian plus a potential

Julián Fernández Bonder^1, and
Leandro M. Del Pezzo^2,

1.
Departamento de Matematica, FCEyN, UBA, 1428 Buenos Aires
2.
Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria (1428), Buenos Aires

Received: December 31, 2005

Revised: April 30, 2006

Published: November 2006

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Abstract

In this paper we study the optimization problem for the first eigenvalue of the $p-$Laplacian plus a potential $V$ with respect to $V$, when the potential is restricted to a bounded, closed and convex set of $L^q(\Omega)$.

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Mathematics Subject Classification: 35P15; Secondary: 49K20.

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