Nonlocal isoperimetric problems
Nonlocal isoperimetric problems
We characterize the volume-constrained minimizers of a nonlocal free energy given by the difference of fractional perimeters. Exploiting the quantitative fractional isoperimetric inequality, we show that balls are the unique minimizers if the volume is sufficiently small, while the existence vs. nonexistence of minimizers for large volumes remains open. We also consider the corresponding isoperimetric problem and prove existence and regularity of minimizers.
- Leibniz Association Germany
- Weierstrass Institute for Applied Analysis and Stochastics Germany
- Weierstrass Institute Germany
ddc:510, 35R11, Fractional perimeter, article, isoperimetric problem, existence, 53A10, 49Q05, fractional perimeter -- isoperimetric problem -- existence -- rigidity and regularity results, 510, rigidity and regularity results
ddc:510, 35R11, Fractional perimeter, article, isoperimetric problem, existence, 53A10, 49Q05, fractional perimeter -- isoperimetric problem -- existence -- rigidity and regularity results, 510, rigidity and regularity results
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