Some Observations on the First Eigenvalue of the p-Laplacian and its Connections with Asymmetry
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In this work, we present a lower bound for the first eigenvalue of the p-Laplacian on bounded domains in ℝ2. Let λ1 be the first eigenvalue and λ1* be the first eigenvalue for the ball of the same volume. Then we show that λ1 ≥ λ1* (1 + Cα(Ω)3), for some constant C, where α is the asymmetry of the domain Ω. This provides a lower bound sharper than the bound in Faber-Krahn inequality.