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Trudinger-Moser type inequalities for weighted Sobolev spaces involving fractional dimensions


Authors: José Francisco de Oliveira and João Marcos do Ó
Journal: Proc. Amer. Math. Soc. 142 (2014), 2813-2828
MSC (2010): Primary 35J62, 46E35, 26D10, 35B33
DOI: https://doi.org/10.1090/S0002-9939-2014-12019-3
Published electronically: May 8, 2014
MathSciNet review: 3209335
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Abstract: We derive sharp Trudinger-Moser inequalities for weighted Sobolev spaces and prove the existence of extremal functions. The inequalities we obtain here extend for fractional dimensions the classical results in the radial case. The main ingredient used in our arguments reveals a new proof of a result due to J. Moser for which we give an improved version.


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Additional Information

José Francisco de Oliveira
Affiliation: Department of Mathematics, Federal University of Pernambuco, 50740-560 Recife, PE, Brazil
Email: oliveira@dmat.ufpe.br

João Marcos do Ó
Affiliation: Department of Mathematics, Federal University of Paraíba, 58051-900 João Pessoa, PB, Brazil
Email: jmbo@pq.cnpq.br

DOI: https://doi.org/10.1090/S0002-9939-2014-12019-3
Received by editor(s): December 29, 2011
Received by editor(s) in revised form: May 19, 2012, and September 8, 2012
Published electronically: May 8, 2014
Additional Notes: This research was partially supported by the National Institute of Science and Technology of Mathematics INCT-Mat, CAPES-PROCAD, CNPq grant 307400/2009-3 and 141853/2012-3, and MCT/CNPq/MEC/CAPES grant 552758/2011-6
Communicated by: Walter Craig
Article copyright: © Copyright 2014 American Mathematical Society