Invertibility versus Lagrange equation for traction free energy-minimal deformations

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7 Scopus citations


Let X Y ⊂ R2 be bounded Jordan domains of the same topological type and a traction free minimal mapping for the Dirichlet energy integral. It is shown that (Formula presented.), restricted to any subdomain (Formula presented.) , is injective if and only if it is harmonic in (Formula presented.) . This result appears pertinent to other energy integrals and, in greater generality, may be interpreted as saying that the interpenetration of matter (under hyperelastic deformations of thin plates) is inevitable precisely in the localities where the Lagrange equation fails.

Original languageEnglish (US)
Pages (from-to)489-496
Number of pages8
JournalCalculus of Variations and Partial Differential Equations
Issue number3-4
StatePublished - Mar 2014


  • Primary 31A05
  • Secondary 35J25

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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