Anisotropic logarithmic Sobolev inequality with a Gaussian weight and its applications
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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.
CitationFeo, F., & Paderni, G. (2019). Anisotropic logarithmic Sobolev inequality with a Gaussian weight and its applications. Electronic Journal of Differential Equations, 2019(89), pp. 1-15.
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