Inthispaperweconsidertwoproblems.Thefirstisconnectedwiththeoptimalrecoveryoffunctionssatisfyiogboundaryconditions.Thesecondisthecharacterizationoftheuniquefunc-tionwhoser-thderivativehasminimumL_∞-norm,takinggivenvaluesofalternatingsignsandsatisfyingboundaryconditions.