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Linear-Growth Functionals

  • Filip RindlerEmail author
Chapter
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Part of the Universitext book series (UTX)

Abstract

After the preparations in the previous chapter, we now return to the task at hand, namely to analyze the following minimization problem for an integral functional with linear growth:
$$ \left\{ \begin{aligned}&\text {Minimize} \quad {\mathscr {F}}[u] := \int _\varOmega f(x, \nabla u(x)) \;\text {d}x\\&\text {over all} \quad \quad u \in \mathrm {W}^{1,1}(\varOmega ;{\mathbb {R}}^m) \,\text {with}\, u|_{\partial \varOmega } = g. \end{aligned} \right. $$
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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK

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