# American Institute of Mathematical Sciences

December  2006, 5(4): 675-690. doi: 10.3934/cpaa.2006.5.675

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

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

Received  January 2006 Revised  May 2006 Published  September 2006

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 $L^q(\Omega)$.
Citation: Julián Fernández Bonder, Leandro M. Del Pezzo. An optimization problem for the first eigenvalue of the $p-$Laplacian plus a potential. Communications on Pure and Applied Analysis, 2006, 5 (4) : 675-690. doi: 10.3934/cpaa.2006.5.675
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