Geometric and transformational properties of Lipschitz domains,Semmes-Kenig-Toro domains,and other classes of finite perimeter domains |
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Authors: | Steve Hofmann Marius Mitrea Michael Taylor |
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Institution: | (1) Department of Mathematics, University of Missouri, 65211 Columbia, MO;(2) Mathematics Department, University of North Carolina, 27599 Chapel Hill, NC |
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Abstract: | In the first part of this article we give intrinsic characterizations of the classes of Lipschitz and C1 domains. Under some mild, necessary, background hypotheses (of topological and geometric measure theoretic nature), we show
that a domain is Lipschitz if and only if it has a continuous transversal vector field. We also show that if the geometric
measure theoretic unit normal of the domain is continuous, then the domain in question is of class C1. In the second part of the article, we study the invariance of various classes of domains of locally finite perimeter under
bi-Lipschitz and C1 diffeomorphisms of the Euclidean space. In particular, we prove that the class of bounded regular SKT domains (previously
called chord-arc domains with vanishing constant, in the literature) is stable under C1 diffeomorphisms. A number of other applications are also presented.
Acknowledgements and Notes. The work of the authors was supported in part by NSF grants DMS-0245401, DMS-0653180, DMS-FRG0456306, and DMS-0456861. |
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Keywords: | Math Subject Classifications" target="_blank">Math Subject Classifications Primary: 49Q15 26B15 49Q25 secondary: 26A16 26A66 26B30 |
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