Some Observations on the First Eigenvalue of the p-Laplacian and its Connections with Asymmetry
Southwest Texas State University, Department of Mathematics
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 λ*1 be the first eigenvalue for the ball of the same volume. Then we show that λ1 ≥ λ*1 (1 + Cα(Ω3)), 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.
Asymmetry, De Giorgi perimeter, p-Laplacian, First eigenvalue, Talenti's inequality
Bhattacharya, 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.