Symmetrization inequalities and Sobolev embeddings

Isoperimetry and Symmetrization for Logarithmic Sobolev Inequalities

Using isoperimetry and symmetrization we provide a unified framework to study the classical and logarithmic Sobolev inequalities. In particular, we obtain new Gaussian symmetrization inequalities and connect them with logarithmic Sobolev inequalities. Our methods are very general and can be easily adapted to more general contexts.

Sobolev Inequalities: Symmetrization and Self Improvement via Truncation

We develop a new method to obtain symmetrization inequalities of Sobolev type. Our approach leads to new inequalities and considerable simplification in the theory of embeddings of Sobolev spaces based on rearrangement invariant spaces.

Symmetrization and Sharp Sobolev Inequalities in Metric Spaces

We derive sharp Sobolev inequalities for Sobolev spaces on metric spaces. In particular, we obtain new sharp Sobolev embeddings and FaberKrahn estimates for Hörmander vector fields.

Pointwise Symmetrization Inequalities for Sobolev Functions and Applications

We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations.

Modified logarithmic Sobolev inequalities and transportation inequalities