On some Variational Problems set on domains tending to infinity

2016/02/08 by Chipot, Michel, Mojsic, Aleksandar, Roy, Prosenjit · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1602.02808

Abstract

Let Ω_ℓ = ℓω₁ × ω₂ where ω₁ ⊂ \R^p and ω₂ ⊂ \R^n-p are assumed to be open and bounded. We consider the following minimization problem: E_{Ω_ℓ}(u_ℓ) = min_{u∈ W0^1,q(Ω_ℓ)}E_{Ω_ℓ}(u) where E_{Ω_ℓ}(u) = ∫_{Ω_ℓ}F(\grad u)-fu, F is a convex function and f∈ L^q'(ω₂). We are interested in studying the asymptotic behavior of the solution u_ℓ as ℓ tends to infinity.

Cited by

• A mixed eigenvalue problem on domains tending to infinity in several directions
• Finsler p-Laplacian in domains becoming unbounded

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