Numerical Methods for Detecting Singular Set Involving the Lavrentiev Phenomenon

Truncation method has been proven to be effective for computing singular minimizers or singular minimizing sequences in variational problems involving the Lavrentiev phenomenon. But truncation area involving the singular set must be selected first when using the truncation method. In this paper three numerical methods for selecting truncation area are introduced, consequently which can detect singular set. Numerical results on Mania's example are given to show the efficiency of the methods.