A Class Of Free Discontinuous Solutions,

We separately deduce the Euler-Lagrange equations of several free discontinuity problems ; when f is put some constraints and u is a scalar functions , we can obtain the dimension estimates of singular set of singular set of minimizer ofby the decay of energy and we generalize the results of L. Ambrosio. N. Fusco & E. Hutchinson. We also discuss the compact properties of collections of singular set of minimizers in Hausdorff meric , and we want to use these results to reduce thedimension of ∑(u).