The energy of the one-dimensional fractional Allen-Cahn layer is continuous and strictly decreasing in the fractional exponent s, with an explicit pole at s=1/2 and an explicit linear expansion at s=1.
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The energy of fractional Allen--Cahn layers in dimension one
The energy of the one-dimensional fractional Allen-Cahn layer is continuous and strictly decreasing in the fractional exponent s, with an explicit pole at s=1/2 and an explicit linear expansion at s=1.