Title data
Christof, Constantin ; Müller, Georg:
A Note on the Equivalence and the Boundary Behavior of a Class of Sobolev Capacities.
Bayreuth
,
2017
. - 27 S.
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NoteOnBoundaryCapacities.pdf - Preprint Available under License Creative Commons BY 4.0: Attribution . Download (581kB) |
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Project financing: |
Bundesministerium für Bildung und Forschung |
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Abstract
The purpose of this paper is to study different notions of Sobolev capacity commonly used in the analysis of obstacle and Signorini type variational inequalities. We review basic facts from nonlinear potential theory in an abstract setting that is tailored to the study of W^{1,p}- and W^{1−1/p,p} - capacities and we prove equivalency results that relate several approaches found in the literature to each other. Motivated by applications in contact mechanics, we especially focus on the behavior of different Sobolev capacities on and near the boundary of the domain in question. As a result, we obtain, for example, that the most common approaches to the sensitivity analysis of Signorini type problems are exactly the same.
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- A Note on the Equivalence and the Boundary Behavior of a Class of Sobolev Capacities. (deposited 25 Jan 2017 08:24) [Currently Displayed]