Smoothness Properties of the Lower Semicontinuous Quasiconvex Envelope
Marcus Wagner
Universität Graz, Austria
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Abstract
Assume that is a convex body with and is a Lipschitz resp. -function. Defining the unbounded function through
we provide sufficient conditions in order to guarantee that its lower semicontinuous quasiconvex envelope
is globally Lipschitz continuous on or differentiable in , respectively. An example shows that the partial derivatives of do not necessarily admit a representation with a “supporting measure” for in .
Cite this article
Marcus Wagner, Smoothness Properties of the Lower Semicontinuous Quasiconvex Envelope. Z. Anal. Anwend. 29 (2010), no. 4, pp. 377–400
DOI 10.4171/ZAA/1413