An optimal Poincare inequality in L^1 for convex domains

By Gabriel Acosta, Ricardo G. Durán. 2003

141 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7cbdd1de4844c22ee142221de7503369c681689e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Cristina Trombetti
2. Carlo Nitsch
3. V. Ferone
4. Andreas Veeser
5. Annalisa Buffa
6. Christoph Ortner
7. Mario Bebendorf
8. Andrea Cianchi

In Geometry and Topology

1. Mario Bebendorf
2. Cristina Trombetti
3. Carlo Nitsch
4. V. Ferone

Citations in the corpus

• Compact embeddings of broken Sobolev spaces and applications (2009, background): “To obtain the second result, we note that the Poincaré inequality on balls takes the form (see Acosta & Duŕan(2004), where this is proved for arbitrary convex sets) ‖u‖L1(B) 6 ρ1‖∇u‖L1(B) ∀ u ∈ W 1,1(B), (u)B = 0.”
• Poincaré constants for finite element stars (2012, background): “Bebendorf [3] if d > 2) and the more recent ones Acosta and Duran [1], Chua and Wheeden [6] show that”
• A remark on optimal weighted Poincar\'e inequalities for convex domains (2012, methodology): “5) is the optimal estimate already obtained in the unweighted case in [1, 2, 13, 23, 31].”
• A Note on the Poincaré Inequality for Convex Domains (2003, background): “The same mistake can also be found in [1], in which the L(1) estimate is considered.”