The ‘‘pathological’’ energy function E(u) 5 u2 for u Þ 0, E(0) 5 1, has no minimizer. As u decreases to 0, the energy also decreases, but there is no way to achieve the value 0. Although examples like this might seem to be unimaginably far from scientific thought, they are at the heart of a new approach (1) to understand the complex microstructure and macroscopic response of materials that unde...
