Generalized Hausdorff dimension distortion in Euclidean spaces under Sobolev mappings

2010/07/13 by Rajala, Tapio, Zapadinskaya, Aleksandra, Zürcher, Thomas · 1 citation
#30C62 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1007.2091

Abstract

We investigate how the integrability of the derivatives of Orlicz-Sobolev mappings defined on open subsets of ℝⁿ affect the sizes of the images of sets of Hausdorff dimension less than n. We measure the sizes of the image sets in terms of generalized Hausdorff measures.

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• On the dimension distortion under fractionally smooth mappings

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