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Indexed by:期刊论文

Date of Publication:2010-01-01

Journal:APPLICABLE ANALYSIS

Included Journals:SCIE

Volume:89

Issue:6

Page Number:915-933

ISSN No.:0003-6811

Key Words:comparison results; regularity; rearrangements; Gauss measure; degenerate elliptic equation

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 nu(x)phi(x), where phi(x) = (2 pi)(-n/2) exp(-vertical bar x vertical bar/(2)) is the density of Gauss measure, nu(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.