Energy barrier and ...-convergence in the ...-dimensional Cahn-Hilliard equation

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).We study the d-dimensional Cahn-Hilliard equation on the flat torus in a parameter regime in which the system size is large and the mean value is close-but not too close-to ...1. We are particularly interested in a quantitative description of the energy landscape in the case in which the uniform state is a local but not global energy minimizer. In this setting, we derive a sharp leading order estimate of the size of the energy barrier surrounding the uniform state. A sharp interface version of the proof leads to a ...-limit of the rescaled energy gap between a given function and the uniform state.