Abstract

*Carl Sundberg* from University of Tennessee-Knoxville conjectured that

where

Our goal is to use a computational approach to investigate if (CSI) holds and to compute the related supremum, assuming it is finite. To do so, we observe that the supremum in (CSI) is equal to:

where

and

The strategy we advocate at the moment is a pretty crude one, namely, tabulate the function in order to get information on the boundedness of the supremum in (CSI). In our lecture, we will discuss the numerical computation of *F*(alpha), the associated problem of Calculus of Variations being solved by a methodology combining a finite difference discretization and an augmented Lagrangian algorithm associated with the following three families of linear constraints v-q_0=0, v'-q_1 =0 and v''-q_2 = 0.

The results of numerical experiments (with a in the range [0,10^6]) will be presented; we will discuss the conclusions we can draw from them concerning the veracity of (CSI).