An isoperimetric inequality for level sets in fractional Sobolev spaces is proven and applied to obtain Hölder regularity in fractional De Giorgi classes.
Imbert,De Giorgi’s regularity theory for elliptic, parabolic and kinetic equations(2026), available at
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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.