We consider the minimizers of the energy ∥u∥ H s 2(Ω) +∫ΩW(u) dx, with s ∈ (0, 1/2), where ∥u∥ Hs(Ω) denotes the total contribution from Ω in the H s norm of u, and W is a double-well potential. By using a fractional Sobolev inequality, we give a new proof of the fact that the sublevel sets of a minimizer u in a large ball BR occupy a volume comparable with the volume of B R.
|Number of pages||13|
|Journal||SIAM Journal on Mathematical Analysis|
|Publication status||Published - 1 Dec 2011|