Minimal energy for elastic inclusions

Hans Knüpfer, Robert V. Kohn

Research output: Contribution to journalArticle


We consider a variant of the isoperimetric problem with a non-local term representingelastic energy. More precisely, our aim is to analyse the optimal energy of an inclusion of a fixed volume the energy of which is determined by surface and elastic energies. This problem has been studied extensively in the physical/metallurgical literature; however, the analysis has mainly been either (i) numerical, or (ii) restricted to a specific set of inclusion shapes, e.g. ellipsoids. In this article, we prove a lower bound for the energy, with no a priori hypothesis on the shape (or even number) of the inclusions. This journal is

Original languageEnglish (US)
Pages (from-to)695-717
Number of pages23
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2127
StatePublished - Mar 8 2011


  • Linear elasticity
  • Phase transformation
  • Precipitate

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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