Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4620600 | Journal of Mathematical Analysis and Applications | 2008 | 10 Pages |
Abstract
In this paper we consider the following class of linear elliptic problems{−div(A(x)∇u)=xNkexp(−|x|22)f(x)inΩ,u=0on∂Ω∖{xN=0}, where k⩾0k⩾0, Ω is a domain (possibly unbounded) of R+N={x=(x1,…,xN)∈RN:xN>0}, f belongs to a suitable weighted Lebesgue space and A(x)=(aij(x))ijA(x)=(aij(x))ij is a symmetric matrix with measurable coefficients satisfyingxNkexp(−|x|22)|ζ|2⩽aij(x)ζiζj⩽CxNkexp(−|x|22)|ζ|2. We compare the solution to such a problem with the solution to a symmetric one-dimensional problem belonging to the same class. Our approach use classical symmetrization methods adapted to a relative isoperimetric inequality with respect to a measure related to the structure of the equation.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
F. Brock, F. Chiacchio, A. Mercaldo,