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The weighted Sobolev and mean value inequalities


Author: Adriano Alves de Medeiros
Journal: Proc. Amer. Math. Soc. 143 (2015), 1229-1239
MSC (2010): Primary 53C42; Secondary 53C21
DOI: https://doi.org/10.1090/S0002-9939-2014-12337-9
Published electronically: November 24, 2014
MathSciNet review: 3293738
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Abstract: In this paper we prove a Michael-Simon inequality in the weighted setting and using this inequality we obtain a diameter control depending of the $ f$-mean curvature, which is based in the work of Topping.


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Additional Information

Adriano Alves de Medeiros
Affiliation: Departamento de Matemática, Universidade Federal da Paraíba, 58051-900, João Pessoa, PB, Brazil
Email: adrianoalves@mat.ufpb.br

DOI: https://doi.org/10.1090/S0002-9939-2014-12337-9
Received by editor(s): April 17, 2013
Received by editor(s) in revised form: May 24, 2013
Published electronically: November 24, 2014
Additional Notes: The author would like to thank Gregorio Pacelli Bessa and Jorge Herbert Soares de Lira for stimulating conversations about this subject.
Dedicated: Dedicated to my son João Gabriel
Communicated by: Lei Ni
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.