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