Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2010-01-01

Journal: APPLICABLE ANALYSIS

Included Journals: SCIE

Volume: 89

Issue: 6

Page Number: 915-933

ISSN: 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.