*THE ‘SLICING’ METHOD
This chapter presents a self-contained account of the slicing method that allows the exhibition of a lower bound for high-dimensional problems through their one-dimensional sections. After computing a family of one-dimensional limit problems, an optimization is performed through an argument characterizing the supremum of a family of measures. The upper inequality is obtained by a density argument whenever recovery sequences have a one-dimensional form. This method can be applied to the high-dimensional gradient theory of phase transitions.
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