Upper bounds for the means of eigenvalues of random boundary value problems with weakly correlated coefficients

Abstract

This paper concerns eigenvalue problems for second-order random differential equations with weakly correlated coefficients. The random problem and the mean (deterministic) problem are embedded in a parametrized problem whose eigenvalues are expanded in a power series in the parameter. This expansion leads, via the variational characterization of the eigenvalues, to computationally accessible upper bounds for the mean values of the eigenvalues of the original problem.