TY - JOUR
T1 - Density estimates for a fluid jet model in the Heisenberg group
AU - Ferrari, Fausto
AU - Valdinoci, Enrico
PY - 2011/10/1
Y1 - 2011/10/1
N2 - In the Heisenberg group setting, we consider the 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 |∇Hnu(ξ)|=Q(ξ), in a suitable weak sense, at the free boundary ξ∈∂{|u|<1}.
AB - In the Heisenberg group setting, we consider the 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 |∇Hnu(ξ)|=Q(ξ), in a suitable weak sense, at the free boundary ξ∈∂{|u|<1}.
KW - Density estimates
KW - Free boundary problems
KW - Heisenberg group
UR - http://www.scopus.com/inward/record.url?scp=79956155957&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2011.04.057
DO - 10.1016/j.jmaa.2011.04.057
M3 - Article
AN - SCOPUS:79956155957
SN - 0022-247X
VL - 382
SP - 448
EP - 468
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -