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Lower estimates for $ p$-moduli and Sobolev class mappings


Author: R. R. Salimov
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 26 (2014), nomer 6.
Journal: St. Petersburg Math. J. 26 (2015), 965-984
MSC (2010): Primary 30C62; Secondary 46E35
Published electronically: September 21, 2015
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Abstract: Finite distortion homeomorphisms on the plane are studied with the help of the moduli techniques. On that basis, a problem that dates back to M. A. Lavrent'ev is solved; this problem concerns estimating the area of the image of a disk under the mappings mentioned above. The asymptotic behavior of such mappings at a point is studied. A condition ensuring the finite Lipschitz property is found.


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Additional Information

R. R. Salimov
Affiliation: Institute of Applied Mathematics and Mechanics, National Academy of Science, 74 Rosa Luksemburg str., 83114 Donetzk, Ukraine
Email: ruslan623@yandex.ru

DOI: https://doi.org/10.1090/spmj/1370
Keywords: $p$-Molude, $p$-capacity, mappings with finite distortion, finite Lipschitzian property
Received by editor(s): January 23, 2014
Published electronically: September 21, 2015
Article copyright: © Copyright 2015 American Mathematical Society