A SYMMETRY RESULT FOR THE ORNSTEIN-UHLENBECK OPERATOR

被引：11

作者：

Cesaroni, Annalisa ^{[1
]}

Novaga, Matteo ^{[2
]}

Valdinoci, Enrico ^{[3
,4
]}

机构：

[1] Univ Padua, Dipartimento Matemat, I-35121 Padua, Italy

[2] Univ Pisa, Dipartimento Matemat, I-56127 Pisa, Italy

[3] Weierstr Inst Angew Anal & Stochast, D-10117 Berlin, Germany

[4] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2014年 / 34卷 / 06期

关键词：

Symmetry results; Ornstein-Uhlenbeck operator; geometric Poincare inequalities; CONJECTURE; GIORGI; SPACES;

D O I：

10.3934/dcds.2014.34.2451

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In 1978 E. De Giorgi formulated a conjecture concerning the one-dimensional symmetry of bounded solutions to the elliptic equation Delta u = F' (u), which are monotone in some direction. In this paper we prove the analogous statement for the equation Delta u - < x, del u > u = F' (u), where the Laplacian is replaced by the Ornstein-Uhlenbeck operator. Our theorem holds without any restriction on the dimension of the ambient space, and this allows us to obtain an similar result in infinite dimensions by a limit procedure.

引用

页码：2451 / 2467

页数：17

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