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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Trudinger-Moser type inequalities for weighted Sobolev spaces involving fractional dimensions
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by José Francisco de Oliveira and João Marcos do Ó PDF
Proc. Amer. Math. Soc. 142 (2014), 2813-2828 Request permission

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
  • MR Author ID: 365349
  • Email: jmbo@pq.cnpq.br
  • 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
  • © Copyright 2014 American Mathematical Society
  • 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
  • MathSciNet review: 3209335