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