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A Note on the Equivalence and the Boundary Behavior of a Class of Sobolev Capacities

URN to cite this document: urn:nbn:de:bvb:703-epub-3290-2

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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Project financing: Bundesministerium für Bildung und Forschung

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.

Further data

Item Type: Preprint, postprint
Keywords: capacity theory; boundary; optimal control; Signorini; variational inequalities;
contact mechanics; sensitivity analysis; nonlinear potential theory; classification problems
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics (Applied Mathematics) > Chair Applied Mathematics (Applied Mathematics) - Univ.-Prof. Dr. Anton Schiela
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-3290-2
Date Deposited: 26 Apr 2017 05:22
Last Modified: 18 Mar 2019 14:21
URI: https://epub.uni-bayreuth.de/id/eprint/3290

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