The minimal gap between Λ2(Ω) and Λ∞(Ω) in a class of convex domains
نویسندگان
چکیده
We consider the minimization problem min Ω∈X (Λ2 − Λ∞) (Ω), where Λ2(Ω) and Λ∞(Ω) are the (square root of the) first eigenvalue of the Laplacian and the first eigenvalue of the ∞−Laplacian respectively. X is the class of convex domains with prescribed diameter. We prove existence of a solution, and we provide several geometrical properties of minimizers.
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