Electron. J. Differential Equations, Vol. 2019 (2019), No. 89, pp. 1-15.

Anisotropic logarithmic Sobolev inequality with a Gaussian weight and its applications

Filomena Feo, Gabriella Paderni

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.

Show me the PDF file (355 KB), TEX file for this article.

Filomena Feo
Dipartimento di Ingegneria
Università degli Studi di Napoli
"Pathenope", Centro Direzionale Isola C4
80143 Napoli, Italy
email: filomena.feo@uniparthenope.it
Gabriella Paderni
Dipartimento di Ingegneria
Università degli Studi di Napoli
"Pathenope", Centro Direzionale Isola C4
80143 Napoli, Italy
email: gabriella.paderni@uniparthenope.it

Return to the EJDE web page