Data di Pubblicazione:
2011
Citazione:
Density estimates for a nonlocal variational model via the Sobolev inequality / O. Savin, E. Valdinoci. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 43:6(2011), pp. 2675-2687.
Abstract:
We consider the minimizers of the energy $\|u\|_{H^s(\Omega)}^2+\int_\Omega W(u)\,dx,$ with $s \in (0,1/2)$, where $\|u\|_{H^s(\Omega)}$ denotes the total contribution from $\Omega$ in the $H^s$ norm of u, and W is a double-well potential. By using a fractional Sobolev inequality, we give a new proof of the fact that the sublevel sets of a minimizer u in a large ball $B_R$ occupy a volume comparable with the volume of $B_R$.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Fractional Laplacian; Geometric properties of minimizers; Phase segregation models
Elenco autori:
O. Savin, E. Valdinoci
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