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.
|Number of pages||29|
|Journal||Journal of Functional Analysis|
|Publication status||Published - 1 Oct 1984|