In the Heisenberg group setting, we consider a fluid jet functional and we prove some density estimates for local minima. In particular, for large r, the measure of the minimal jet in balls of radius r centered at the jet is of the order of rQ−1, while the measure of the exterior medium is of the order of rQ, where Q=2(n+1) is the homogeneous dimension. Also, we obtain that , in a suitable weak sense, at the free boundary ξ∈∂{|u|<1}.
F. Ferrari, E. Valdinoci (2011). Density estimates for a fluid jet model in the Heisenberg group. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 382, 448-468 [10.1016/j.jmaa.2011.04.057].
Density estimates for a fluid jet model in the Heisenberg group
FERRARI, FAUSTO;
2011
Abstract
In the Heisenberg group setting, we consider a fluid jet functional and we prove some density estimates for local minima. In particular, for large r, the measure of the minimal jet in balls of radius r centered at the jet is of the order of rQ−1, while the measure of the exterior medium is of the order of rQ, where Q=2(n+1) is the homogeneous dimension. Also, we obtain that , in a suitable weak sense, at the free boundary ξ∈∂{|u|<1}.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.