A SYMMETRY RESULT FOR DEGENERATE ELLIPTIC EQUATIONS ON THE WIENER SPACE WITH NONLINEAR BOUNDARY CONDITIONS AND APPLICATIONS

被引：3

作者：

Novaga, Matteo ^{[1
]}

Pallara, Diego ^{[2
,3
]}

Sire, Yannick ^{[4
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy

[2] Univ Salento, Dipartimento Matemat & Fis Ennio De Giorgi, POB 193, I-73100 Lecce, Italy

[3] Univ Salento, Ist Nazl Fis Nucl, POB 193, I-73100 Lecce, Italy

[4] Univ Aix Marseille, I2M, CNRS, UMR 7353, Marseille, France

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2016年 / 9卷 / 03期

关键词：

Fractional Ornstein-Uhlenbeck operator; Wiener spaces; EXTENSION PROBLEM; CONJECTURE; GIORGI; INEQUALITY; REGULARITY;

D O I：

10.3934/dcdss.2016030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to study a boundary reaction problem on the space X x R, where X is an abstract Wiener space. We prove that smooth bounded solutions enjoy a symmetry property, i.e., are one-dimensional in a suitable sense. As a corollary of our result, we obtain a symmetry property for some solutions of the following equation (-Delta(gamma))(s)u = f(u), with s is an element of (0, 1), where (-Delta(gamma))(s) denotes a fractional power of the Ornstein-Uhlenbeck operator, and we prove that for any s is an element of (0, 1) monotone solutions are one-dimensional.

引用

页码：815 / 831

页数：17

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