JIPAM

Linear Elliptic Equations and Gauss Measure  
 
  Authors: G. di Blasio,  
  Keywords: Linear elliptic equation, Comparison theorem, Rearrangements of functions, Gauss measure.  
  Date Received: 20/02/03  
  Date Accepted: 30/06/03  
  Subject Codes:

35B05, 35J70.

  
  Editors: Alberto Fiorenza,  
 
  Abstract:

In this paper we study a Dirichlet problem relative to a linear elliptic equation with lower-order terms, whose ellipticity condition is given in terms of the function $ varphi (x)=(2pi )^{-frac{n}{2}}$$ expleft( -leftvert xrightvert ^{2}/2right) $, the density in the Gaussian measure. Using the notion of rearrangement with respect to the 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.
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