کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1156980 958906 2008 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Hypoelliptic heat kernel inequalities on Lie groups
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Hypoelliptic heat kernel inequalities on Lie groups
چکیده انگلیسی

This paper discusses the existence of gradient estimates for the heat kernel of a second order hypoelliptic operator on a manifold. For elliptic operators, it is now standard that such estimates (satisfying certain conditions on coefficients) are equivalent to a lower bound on the Ricci tensor of the Riemannian metric. For hypoelliptic operators, the associated “Ricci curvature” takes on the value −∞−∞ at points of degeneracy of the semi-Riemannian metric. For this reason, the standard proofs for the elliptic theory fail in the hypoelliptic setting.This paper presents recent results for hypoelliptic operators. Malliavin calculus methods transfer the problem to one of determining certain infinite dimensional estimates. Here, the underlying manifold is a Lie group, and the hypoelliptic operators are given by the sum of squares of left invariant vector fields. In particular, “LpLp-type” gradient estimates hold for p∈(1,∞)p∈(1,∞), and the p=2p=2 gradient estimate implies a Poincaré estimate in this context.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 118, Issue 3, March 2008, Pages 368–388
نویسندگان
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