Extension of convex functions from a hyperplane to a half-space

John M. Ball*, Christopher L. Horner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

It is shown that a possibly infinite-valued proper lower semicontinuous convex function on Rn has an extension to a convex function on the half-space Rn×[0, ∞) which is finite and smooth on the open half-space Rn×(0, ∞). The result is applied to nonlinear elasticity, where it clarifies how the condition of polyconvexity of the free-energy density ψ(Dy) is best expressed when ψ(A)→∞ as detA→0+.
Original languageEnglish
Article number107
JournalCalculus of Variations and Partial Differential Equations
Volume63
Issue number4
Early online date17 Apr 2024
DOIs
Publication statusPublished - May 2024

Keywords

  • 74B20
  • 49J45
  • 26B25

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