On the Non‐Polyhedricity of Sets with Upper and Lower Bounds in Dual Spaces. Issue 4 (16th April 2018)

• Record Type: Journal Article
• Authors: Christof, Constantin; Wachsmuth, Gerd
• Is Part Of: Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik. Volume 40:Issue 4(2017)
• Page Start: 339
• Page End: 350
• Publication Date: 2018-04-16
• Subjects: Polyhedricity -- Frictional Contact Problems -- Variational Inequalities of the Second Kind -- Directional Differentiability -- Sensitivity Analysis; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; 510.5
• DOI: 10.1002/gamm.201740005
• Languages: English
• ISSNs: 0936-7195

Abstract

Abstract: We demonstrate that the set L ∞ ( X, [−1, 1]) of all measurable functions over a Borel measure space ( X, B, μ) with values in the unit interval is typically non‐polyhedric when interpreted as a subset of a dual space. Our findings contrast the classical result that subsets of Dirichlet spaces with pointwise upper and lower bounds are polyhedric. In particular, additional structural assumptions are unavoidable when the concept of polyhedricity is used to study the differentiability properties of solution maps to variational inequalities of the second kind in, e.g., the spaces H 1/2 (∂Ω) or H 0 1 (Ω).