Pointwise Symmetrization Inequalities for Sobolev functions and applications

Abstract

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

made a number of corrections, added some references

References in corpus (6)

• Isoperimetric and Concentration Inequalities - Equivalence under Curvature Lower Bound
• Sobolev Inequalities: Symmetrization and Self Improvement via Truncation
• Isoperimetry and symmetrization for logarithmic Sobolev inequalities
• On the role of Convexity in Functional and Isoperimetric Inequalities
• An isoperimetric inequality on the ${\ell }_p$ balls
• Self Improving Sobolev-Poincare Inequalities, Truncation and Symmetrization

Cited by in corpus (6)

• Boundedness of classical operators on rearrangement-invariant spaces
• Isoperimetric weights and generalized uncertainty inequalities in metric measure spaces
• Optimal Sobolev embeddings for the Ornstein-Uhlenbeck operator
• Compactness of higher-order Sobolev embeddings
• Integral isoperimetric transference and dimensionless Sobolev inequalities
• Factoring Sobolev inequalities through classes of functions