Density estimates for a fluid jet model in the Heisenberg group

作者：Ferrari Fausto^*; Valdinoci Enrico

来源：Journal of Mathematical Analysis and Applications, 2011, 382(1): 448-468.

DOI：10.1016/j.jmaa.2011.04.057

• Heisenberg group
• Free boundary problems
• Density estimates

In the Heisenberg group setting, we consider the fluid jet functional
integral vertical bar del H-n W(xi)vertical bar(2) + Q(xi) chi({vertical bar w vertical bar<1}) (xi) d xi
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 r(Q-1), while the measure of the exterior medium is of the order of r(Q), where Q = 2(n + 1) is the homogeneous dimension. Also, we obtain that vertical bar del H(n)u(xi)vertical bar = root Q(xi), in a suitable weak sense, at the free boundary xi is an element of partial derivative {vertical bar u vertical bar < 1).

• 出版日期2011-10-1