Poincaré Inequalities and Neumann Problems for the p-Laplacian
Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 738-753
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We prove an equivalence between weighted Poincaré inequalities and the existence of weak solutions to a Neumann problem related to a degenerate $p$ -Laplacian. The Poincaré inequalities are formulated in the context of degenerate Sobolev spaces defined in terms of a quadratic form, and the associated matrix is the source of the degeneracy in the $p$ -Laplacian.
Mots-clés :
30C65, 35B65, 35J70, 42B35, 42B37, 46E35, degenerate Sobolev space, p-Laplacian, Poincaré inequalities
Cruz-Uribe, David; Rodney, Scott; Rosta, Emily. Poincaré Inequalities and Neumann Problems for the p-Laplacian. Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 738-753. doi: 10.4153/CMB-2018-001-6
@article{10_4153_CMB_2018_001_6,
author = {Cruz-Uribe, David and Rodney, Scott and Rosta, Emily},
title = {Poincar\'e {Inequalities} and {Neumann} {Problems} for the {p-Laplacian}},
journal = {Canadian mathematical bulletin},
pages = {738--753},
year = {2018},
volume = {61},
number = {4},
doi = {10.4153/CMB-2018-001-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-001-6/}
}
TY - JOUR AU - Cruz-Uribe, David AU - Rodney, Scott AU - Rosta, Emily TI - Poincaré Inequalities and Neumann Problems for the p-Laplacian JO - Canadian mathematical bulletin PY - 2018 SP - 738 EP - 753 VL - 61 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-001-6/ DO - 10.4153/CMB-2018-001-6 ID - 10_4153_CMB_2018_001_6 ER -
%0 Journal Article %A Cruz-Uribe, David %A Rodney, Scott %A Rosta, Emily %T Poincaré Inequalities and Neumann Problems for the p-Laplacian %J Canadian mathematical bulletin %D 2018 %P 738-753 %V 61 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-001-6/ %R 10.4153/CMB-2018-001-6 %F 10_4153_CMB_2018_001_6
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