Data di Pubblicazione:
2015
Citazione:
Nonlocal quantitative isoperimetric inequalities / A. Di Castro, M. Novaga, B. Ruffini, E. Valdinoci. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 54:3(2015), pp. 2421-2464. [10.1007/s00526-015-0870-x]
Abstract:
We show a quantitative-type isoperimetric inequality for fractional perimeters where the deficit of the t-perimeter, up to multiplicative constants, controls from above that of the s-perimeter, with s smaller than t. To do this we consider a problem of independent interest: we characterize the volume-constrained minimizers of a nonlocal free energy given by the difference of the t-perimeter and the s-perimeter. In particular, we show that balls are the unique minimizers if the volume is sufficiently small, depending on t-s, 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 for all s,t. When s=0 this problem reduces to the fractional isoperimetric problem, for which it is well known that balls are the only minimizers.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
35R11; 49Q05; 53A10; Analysis; Applied Mathematics
Elenco autori:
A. Di Castro, M. Novaga, B. Ruffini, E. Valdinoci
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