Bhattacharya, Tilak2020-06-032020-06-032001-05-16Bhattacharya, T. (2001). Some observations on the first eigenvalue of the p-Laplacian and its connections with asymmetry. <i>Electronic Journal of Differential Equations, 2001</i>(35), pp. 1-15.1072-6691https://hdl.handle.net/10877/11106In 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 λ*1 be the first eigenvalue for the ball of the same volume. Then we show that, λ1 ≥ λ*1 (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.Text15 pages1 file (.pdf)enAttribution 4.0 InternationalAsymmetryDe Giorgi perimeterp-LaplacianFirst eigenvalueTalenti's inequalityArticle