Eigenvalue homogenization problem with indefinite weights

2015/04/15 by Bonder, J. Fernández, Pinasco, J. P., Salort, A. M.
#35B27 #35P15 #35P30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1504.03893

Abstract

In this work we study the homogenization problem for nonlinear elliptic equations involving p-Laplacian type operators with sign changing weights. We study the asymptotic behavior of variational eigenvalues, which consist on a double sequence of eigenvalues. We show that the k-th positive eigenvalue goes to infinity when the average of the weight is nonpositive, and converge to the k-th variational eigenvalue of the limit problem when the average is positive for any k≥ 1.

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