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Analytical Background

  • Sören BartelsEmail author
Chapter
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 47)

Abstract

The calculus of variations provides an attractive mathematical framework for describing many phenomena in continuum mechanics. In this chapter model problems, including bending thin elastic objects as well as elastoplastic material behavior, are formulated within this framework, and general concepts such as the direct method in the calculus of variations and gradient flows that imply their well-posedness are discussed. The definitions and most important properties of Sobolev and Sobolev–Bochner spaces are provided.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Abteilung für Angewandte MathematikAlbert-Ludwigs-Universität FreiburgFreiburgGermany

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