Topological rearrangement of a function |
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| Institution: | 1. Dipartimento di Matematica, “La Sapienza”, Piazzale Aldo Moro 2, Roma, 00185, Italia;2. Department of Mathematics, University of Wisconsin, Richland Center, Wisconsin, USA;1. Leibniz Institute for Solid State and Materials Research (IFW) Dresden, Helmholtzstrasse 20, D-01069 Dresden, Germany;2. Institute for Materials Science, TU Dresden, 01062 Dresden, Germany;3. Institute of Natural Sciences, Ural Federal University, 620002 Ekaterinburg, Russia;4. Nippon Steel and Sumitomo Metal Corporation, Futtsu, Japan;1. School of Chemistry and Environment, South China Normal University, Guangzhou 510006, China;2. EVE Energy Co. Ltd., Huizhou 516006, China;1. Institute of Physics, Faculty of Sciences, P.J. Safarik University, Park Angelinum 9, 041 54 Kosice, Slovakia;2. Institute for Materials Science, Kiel University, Kaiserstraße 2, 24143 Kiel, Germany;3. CPM-TIP, P.J. Safarik University, Park Angelinum 9, 041 54 Kosice, Slovakia |
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| Abstract: | We extend our results on weak diffeomorphism classes and decompositions of Sobolev functions to a more general framework. We introduce a family of decompositions of Sobolev functions W01,p rich enough that we conjecture it allows decomposition of all Sobolev functions, not just the “craterless” ones considered in 7]. The associated weak diffeomorphism classes of a W01,p Sobolev function are weakly closed when p ≥ n. |
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