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Generalized dimension estimates for images of porous sets under monotone Sobolev mappings


Authors: Pekka Koskela and Aleksandra Zapadinskaya
Journal: Proc. Amer. Math. Soc. 143 (2015), 2033-2042
MSC (2010): Primary 46E35, 26B10, 28A78
DOI: https://doi.org/10.1090/S0002-9939-2014-12371-9
Published electronically: December 4, 2014
MathSciNet review: 3314112
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Abstract: We give an essentially sharp estimate in terms of generalized Hausdorff measures for images of porous sets under monotone Sobolev mappings, satisfying suitable Orlicz-Sobolev conditions.


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Additional Information

Pekka Koskela
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), FI-40014, Finland
Email: pkoskela@maths.jyu.fi

Aleksandra Zapadinskaya
Affiliation: Department of Mathematical Sciences, University of Cincinnati, 4199 French Hall West, 2815 Commons Way, Cincinnati, Ohio 45221-0025
Address at time of publication: Department of Mathematics, University of Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
Email: zapadiay@uc.edu, azapadinskaya@mail.dm.unipi.it

DOI: https://doi.org/10.1090/S0002-9939-2014-12371-9
Keywords: Sobolev mapping, Orlicz-Sobolev mapping, generalized Hausdorff measure, monotone mapping
Received by editor(s): March 13, 2013
Received by editor(s) in revised form: September 25, 2013
Published electronically: December 4, 2014
Additional Notes: The authors were partially supported by the Academy of Finland grants 131477 and 263850.
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.