Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 89, pp. 1-15.

Title: Anisotropic logarithmic Sobolev inequality
       with a Gaussian weight and its applications

Authors: Filomena Feo      (Univ. degli Studi di Napoli, Italy)
         Gabriella Paderni (Univ. degli Studi di Napoli, Italy)
 
Abstract:
 In this article we prove a Logarithmic Sobolev type inequality and
 a Poincare type inequality for functions in the anisotropic
 Gaussian Sobolev space. As an application we study a class of equations,
 whose anisotropic elliptic condition is given in term of the density of
 Gauss measure. Finally some extensions of the main results are given
 for a class of weighted (not Gaussian one) anisotropic Sobolev spaces. 

Submitted February 7, 2019. Published July 17, 2019.
Math Subject Classifications: 46E35, 35A12, 46E30.
Key Words: Gauss measure; logarithmic Sobolev-Poincare inequality;
           anisotropic spaces.