Density estimates for a fluid jet model in the Heisenberg group

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:382

Article

Ferrari, Fausto¹  Valdinoci, Enrico² 

[1] Univ Bologna, Dipartmento Matemat, I-40126 Bologna, Italy

[2] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

关键词: Heisenberg group;    Free boundary problems;    Density estimates;   

DOI  :  10.1016/j.jmaa.2011.04.057

来源: Elsevier

【 摘 要 】

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). (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free