An isoperimetric inequality for level sets in fractional Sobolev spaces is proven and applied to obtain Hölder regularity in fractional De Giorgi classes.
Giusti,Minimal surfaces and functions of bounded variation, Monographs in Mathematics, vol
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A fractional De Giorgi isoperimetric type inequality
An isoperimetric inequality for level sets in fractional Sobolev spaces is proven and applied to obtain Hölder regularity in fractional De Giorgi classes.