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Applicable Analysis
An International Journal
Volume 89, 2010 - Issue 6
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Original Articles

Comparison and regularity results for degenerate elliptic equations related to Gauss measure

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Pages 915-933 | Received 17 Jan 2009, Accepted 03 Feb 2010, Published online: 18 May 2010
 

Abstract

This article deals with a Dirichlet problem relative to a linear elliptic equation with zero-order terms, whose ellipticity condition is given in terms of the function ν(x)ϕ(x), where is the density of Gauss measure, ν(x) is a nonnegative integrable function. Using the notion of rearrangement with respect to 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. Also, some regularity results for the solutions in Lorentz–Zygmund spaces are obtained by us.

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Acknowledgements

This project was supported by NSFC(No:10401009) and NCET of China (No:060275).

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