On the minimization of some nonconvex double obstacle problems

[摘要] We consider a nonconvex variational problem for which the set ofadmissible functions consists of all Lipschitz functions locatedbetween two fixed obstacles. It turns out that the value of theminimization problem at hand is equal to zero when the obstaclesdo not touch each other; otherwise, it might be positive. Theresults are obtained through the construction of suitableminimizing sequences. Interpolating these minimizing sequences insome discrete space, a numerical analysis is then carried out.

[学科分类] 应用数学