Monotonicity Results for the Principal Eigenvalue of the Generalized Robin Problem
نویسندگان
چکیده
We study domain monotonicity of the principal eigenvalue λ1 (α) corresponding to ∆u = λ(α)u in Ω, ∂u ∂ν = αu on ∂Ω, with Ω ⊂ Rn a C0,1 bounded domain, and α a fixed real. We show that contrary to intuition domain monotonicity might hold if one of the two domains is a ball.
منابع مشابه
Bounds and monotonicity for the generalized Robin problem
Abstract. We consider the principal eigenvalue λ 1 (α) corresponding to ∆u = λ(α)u in Ω, ∂u ∂ν = αu on ∂Ω, with α a fixed real, and Ω ⊂ R a C bounded domain. If α > 0 and small, we derive bounds for λ 1 (α) in terms of a Stekloff-type eigenvalue; while for α > 0 large we study the behavior of its growth in terms of maximum curvature. We analyze how domain monotonicity of the principal eigenvalu...
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