A rearrangement based proof for the existence of extremal functions for the Sobolev-Poincaré inequality on \(B^n\)

DOI10.1016/J.JMAA.2009.09.050zbMath1185.26029OpenAlexW2074495189MaRDI QIDQ1046522

Mark Leckband

Publication date: 22 December 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.09.050

zbMATH Keywords

rearrangementextremalsSobolev-Poincaré inequality

Mathematics Subject Classification ID

Inequalities involving derivatives and differential and integral operators (26D10) Applications of functional analysis to differential and integral equations (46N20)

Related Items (2)

Poincaré trace inequalities in \(BV({\mathbb {B}}^n)\) with non-standard normalization ⋮ Balls minimize trace constants in BV

Cites Work

• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• A sharp form of Poincaré type inequalities on balls and spheres
• Sur une généralisation de l'inégalité de Wirtinger. (A generalization of Wirtinger's inequality)
• Best constant in Sobolev inequality
• Problèmes isoperimetriques et espaces de Sobolev
• A symmetry problem related to Wirtinger's and Poincaré's inequality
• The shape of extremal functions for Poincaré-Sobolev-type inequalities in a ball
• Zerlegung konvexer Körper durch minimale Trennflächen.
• Moser's inequality on the ball Bⁿ for functions with mean value zero
• On the existence of extremal functions in Sobolev embedding theorems with critical exponents
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