W1,p-quasiconvexity and variational problems for multiple integrals

J. M. Ball, F. Murat

Research output: Contribution to journalArticle

Abstract

Variational problems for the multiple integral IO(u) = ?O g(?u(x))dx, where O?Rm and u:O?Rn are studied. A new condition on g, called W1,p-quasiconvexity is introduced which generalizes in a natural way the quasiconvexity condition of C. B. Morrey, it being shown in particular to be necessary for sequential weak lower semicontinuity of IO in W1,p(O;Rn) and for the existence of minimizers for certain related integrals. Counterexamples are given concerning the weak continuity properties of Jacobians in W1,p(O;Rn), p = n = m. An existence theorem for nonlinear elastostatics is proved under optimal growth hypotheses. © 1984.

Original languageEnglish
Pages (from-to)225-253
Number of pages29
JournalJournal of Functional Analysis
Volume58
Issue number3
Publication statusPublished - 1 Oct 1984

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