Homogenization of Fucik eigenvalues by optimal partition methods

2016/01/25 by Ariel M. Salort, Salort, Ariel M.
Mathematics · #34A08 #35B27 #35P15 #35P30 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:34A08 #msc:35B27 #msc:35P15 #msc:35P30

paper · pdf · doi:10.48550/arxiv.1601.06753

13 pages

arxiv created 2016/01/25 · arxiv updated 2016/01/26

Abstract

Given a bounded domain Ω in ℝ^N, N≥ 1 we study the asymptotic behavior as ε → 0 of the eigencurves of -Δ_p u_ε=α_ε m(\tfracxε)(u_ε⁺ )^p-1 - β_ε n(\tfracxε)(u_ε^- )^p-1 \textrm in Ω with Dirichlet boundary conditions, where m and n are bounded periodic weights. In this work we obtain accurate bounds of the convergence rates of these curves to some limit curves as ε → 0.

Related

• Homogenization of Fučík eigencurves
• Convergence rates in a weighted Fucik problem
• Quantitative homogenization of principal Dirichlet eigenvalue shape optimizers
• Eigenvalue homogenization for quasilinear elliptic equations with different boundary conditions
• First-order expansion for the Dirichlet eigenvalues of an elliptic system with oscillating coefficients