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

Pages: 675 - 690, Volume 5, Issue 4, December 2006

doi:10.3934/cpaa.2006.5.675       Abstract        Full Text (175.4K)       Related Articles

Julián Fernández Bonder - Departamento de Matematica, FCEyN, UBA, 1428 Buenos Aires, Argentina (email)
Leandro M. Del Pezzo - Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria (1428), Buenos Aires, Argentina (email)

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 $L^q(\Omega)$.

Keywords:  $p-$Laplacian, nonlinear eigenvalues, minimization problems.
Mathematics Subject Classification:  35P15; Secondary: 49K20.

Received: January 2006;      Revised: May 2006;      Published: September 2006.