In this paper we prove a comparison result for weak solutions to linear elliptic problems of the type -(a(ij) (x)u(xi))(xj) = f (x)phi(x) in Omega u = 0 on partial derivativeOmega. where Omega is an open set of R-n (n greater than or equal to 2). phi(x) = (2pi,7)(-n/2) exp(-\x(2)/2), a(ij)(x) are measurable functions such that a(ij) (x)xi(i)xi(j) greater than or equal to phi(x)\xi(2) a.e. x is an element of Omega. xi is an element of R-n and f(x) is a measurable function taken in order to guarantee the existence of a solution u is an element of H-0(1) (phi, Omega) of (1.1). We use the notion of rearrangement related to Gauss measure to compare it (x) with the solution of a problem of the same type, whose data are defined in a half-space and depend only on one variable.

### A comparison result related to Gauss measure

#### Abstract

In this paper we prove a comparison result for weak solutions to linear elliptic problems of the type -(a(ij) (x)u(xi))(xj) = f (x)phi(x) in Omega u = 0 on partial derivativeOmega. where Omega is an open set of R-n (n greater than or equal to 2). phi(x) = (2pi,7)(-n/2) exp(-\x(2)/2), a(ij)(x) are measurable functions such that a(ij) (x)xi(i)xi(j) greater than or equal to phi(x)\xi(2) a.e. x is an element of Omega. xi is an element of R-n and f(x) is a measurable function taken in order to guarantee the existence of a solution u is an element of H-0(1) (phi, Omega) of (1.1). We use the notion of rearrangement related to Gauss measure to compare it (x) with the solution of a problem of the same type, whose data are defined in a half-space and depend only on one variable.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11367/24939
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