An invitation to n-harmonic hyperelasticity

Tadeusz Iwaniec, Jani Onninen, Fred W. Gehring

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

We give an account of some recent developments in which quasiconformal theory and nonlinear elasticity share common problems of compelling mathematical interest. Geometric function theory is currently a field of enormous activity where the language and general framework of nonlinear elasticity is extremely fruitful and significant. As this interplay developed n-harmonic deformations became valid and well acknowledged as generalization of conformal mappings in Rn. We have also found a place for n-harmonic deformations in the theory of hyperelasticity. J. Ball's fundamental paper [5] accounts for the principles of hyperelasticity and sets up mathematical problems. In presenting the recent advances we have relied on a few new existing articles [2, 3, 28, 29, 30, 31, 32, 33].

Original languageEnglish (US)
Pages (from-to)319-343
Number of pages25
JournalPure and Applied Mathematics Quarterly
Volume7
Issue number2
DOIs
StatePublished - Apr 2011

Keywords

  • Extremal problems
  • Free lagrangians
  • N-harmonics
  • Quasiconformal mappings
  • Variational integrals

ASJC Scopus subject areas

  • Mathematics(all)

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