Electron. J. Diff. Equ., Vol. 2015 (2015), No. 05, pp. 1-17.

Comparison results for elliptic variational inequalities related to Gauss measure

Yujuan Tian, Chao Ma

Abstract:
In this article, we study linear elliptic variational inequalities that are defined on a possibly unbounded domain and whose ellipticity condition is given in terms of the density of Gauss measure. Using the notion of rearrangement with respect to the Gauss measure, we prove a comparison result with a problem of the same type defined in a half space, with data depending only on the first variable.

Submitted November 19, 2014. Published January 5, 2015.
Math Subject Classifications: 35J86, 35J70, 35B45.
Key Words: Comparison results; rearrangements; gauss measure; Elliptic variational inequality.

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Yujuan Tian
School of Mathematical Sciences, Shandong Normal University
Jinan, Shandong 250014, China
email: tianyujuan0302@126.com
Chao Ma
School of Mathematical Sciences, University of Jinan
Jinan, Shandong 250022, China
email: chaos_ma@163.com

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