The method of moments for some one-dimensional, non-local, non-convex variational problems

Abstract

We focus on the analysis of homogeneous, non-convex, non-local variational principles given in the general form: min u ∫ ∫ J × J W ( u ′ ( x ) , u ′ ( y ) ) d x d y where W can be expressed as a polynomial. This work extends previous result of Pedregal (1997) [19] by using moments of parametrized measures to transform the generalized form of the problem in terms of Young measures into a more convenient mathematical program with quadratic and conic structure.