Feo, FilomenaPaderni, Gabriella2021-11-292021-11-292019-07-17Feo, F., & Paderni, G. (2019). Anisotropic logarithmic Sobolev inequality with a Gaussian weight and its applications. <i>Electronic Journal of Differential Equations, 2019</i>(89), pp. 1-15.1072-6691https://hdl.handle.net/10877/14977In 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.Text15 pages1 file (.pdf)enAttribution 4.0 InternationalGauss measureLogarithmic Sobolev-Poincare inequalityAnisotropic spacesArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.