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Poincaré Inequalities and Neumann Problems for the p-Laplacian

Published online by Cambridge University Press:  20 November 2018

David Cruz-Uribe ,
Scott Rodney  and
Emily Rosta
David Cruz-Uribe
Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487, USA, e-mail : dcruzuribe@ua.edu
Scott Rodney
Affiliation:
Dept. of Mathematics, Physics and Geology, Cape Breton University, Sydney, Nova Scotia B1Y3V3, e-mail : scott_rodney@cbu.ca, emily_charlotte8@hotmail.com
Emily Rosta
Affiliation:
Dept. of Mathematics, Physics and Geology, Cape Breton University, Sydney, Nova Scotia B1Y3V3, e-mail : scott_rodney@cbu.ca, emily_charlotte8@hotmail.com
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Abstract

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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.

Keywords

30C6535B6535J7042B3542B3746E35degenerate Sobolev spacep-LaplacianPoincaré inequalities
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 4 , 01 December 2018 , pp. 738 - 753
Copyright
Copyright © Canadian Mathematical Society 2018

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