Abstract:
We show the exponential integrability and transportation cost related to logarithmic Sobolev inequalities .We investigate the continuous rearrangement and symmetry of solutions of elliptic problems .
The symmetry of solutions of p-Laplace equations in the Euclidean space is considered . We study the generalization of an inequality by Talagrand and Links' with the logarithmic Sobolev inequality . We also show the optimal Euclidean Sobolev logarithmic inequality and the Hardy type integral inequality associated with the generalized translation We give the log- Sobolev inequalities and regions with exterior exponential cusps and spectral gabs .