Numeric estimates of the principal eigenvalue of the p-Laplacian using interval arithmetic

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