Some_examples_of_calculus_of_variations_of_discontinuous_functions_and_their_implications.pdf

We consider functions defined on [0, L] with special jump discontinuities, and discuss two different methods of doing calculus of variations. One method is to solve the boundary value problem in each sub-region divided by the discontinuities, and the other method is to use Fourier series on the whole region. We argue that the second method, though has an energy divergence problem, can lead to a unified view of similar examples and may provide a way of studying nematic defects.