Abstract
We present a numerical algorithm for computing rigorous upper and lower estimates of the principal eigenvalue of the p-Laplacian. To control all possible errors including the rounding errors of the computer arithmetic, we use the interval arithmetic. We implement our algorithm in the Julia programming language using IntervalArithmetic.jl package [12].
See also https://ejde.math.txstate.edu/special/02/b3/abstr.html
Reference15 articles.
1. Allegretto, W.; Huang, Y. X.; A Picones identity for the p-Laplacian and applications. Nonlinear Anal. 32 (1998), 819-830.
2. Benedikt, J.; Drabek, P.; Estimates of the principal eigenvalue of the p-Laplacian. J. Math. Anal. Appl. 393 (2012), 311-315.
3. Benedikt, J.; Drabek, P.; Asymptotics for the principal eigenvalue of the p-Laplacian on the ball as p approaches 1. Nonlinear Anal. 93 (2013), 23-29.
4. Benedikt, J.; Girg, P.; Kotrla, L.; Takac, P.; Origin of the p-Laplacian and A. Missbach. Electron. J. Differential Equations (2018), paper no. 16, 17 pp.
5. Biezuner, R. J.; Brown, J.; Ercole, G.; Martins, E. M.; Computing the first eigenpair of the p-Laplacian via inverse iteration of sublinear supersolutions, J. Sci. Comput. 52 (2012) 180-201.