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 / M. F., Betta; F., Brock; Mercaldo, Anna; Posteraro, MARIA ROSARIA. - In: COMPTES RENDUS MATHÉMATIQUE. - ISSN 1631-073X. - STAMPA. - 334:6(2002), pp. 451-456. [10.1016/S1631-073X(02)02295-1]

A comparison result related to Gauss measure

MERCALDO, ANNA;POSTERARO, MARIA ROSARIA
2002

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.
2002
A comparison result related to Gauss measure / M. F., Betta; F., Brock; Mercaldo, Anna; Posteraro, MARIA ROSARIA. - In: COMPTES RENDUS MATHÉMATIQUE. - ISSN 1631-073X. - STAMPA. - 334:6(2002), pp. 451-456. [10.1016/S1631-073X(02)02295-1]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/205345
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 28
  • ???jsp.display-item.citation.isi??? 33
social impact