Sobolev Inequalities: Symmetrization and Self Improvement via Truncation

Abstract

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.

16 pages

References in corpus (1)

• Symmetrization and sharp Sobolev inequalities in metric spaces

Cited by in corpus (6)

• Pointwise Symmetrization Inequalities for Sobolev functions and applications
• Isoperimetry and symmetrization for logarithmic Sobolev inequalities
• Self Improving Sobolev-Poincare Inequalities, Truncation and Symmetrization
• A note on self improvement of Poincaré-Sobolev inequalities via Garsia-Rodemich spaces
• Integral isoperimetric transference and dimensionless Sobolev inequalities
• Factoring Sobolev inequalities through classes of functions