An isoperimetric inequality for level sets in fractional Sobolev spaces is proven and applied to obtain Hölder regularity in fractional De Giorgi classes.
Giusti,Direct methods in the calculus of variations, World Scientific Publishing Co., Inc., River Edge, NJ, 2003
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Proves local Calderón-Zygmund estimates for gradients of solutions to singular double-phase elliptic measure data problems for 2-1/n < p < 2 under natural assumptions on p, q, and a(x).
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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.
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Gradient estimates for singular elliptic measure data problems with double phase
Proves local Calderón-Zygmund estimates for gradients of solutions to singular double-phase elliptic measure data problems for 2-1/n < p < 2 under natural assumptions on p, q, and a(x).