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

作者：Aranda E^*; Meziat R J

来源：Journal of Mathematical Analysis and Applications, 2011, 382(1): 314-323.

DOI：10.1016/j.jmaa.2011.04.052

• Moments
• Non-local variational problems
• Semidefinite programming

We focus on the analysis of homogeneous, non-convex, non-local variational principles given in the general form:
min(u) integral integral(integral x integral) W (u'(x), u' (y)) dx dy
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.

• 出版日期2011-10-1