Some remarks about the \(p\)-Dirichlet integral. (English) Zbl 0808.49038

Giaquinta, Mariano; Modica, Giuseppe; Souček, Jiří

Commentat. Math. Univ. Carol. 35, No. 1, 55-62 (1994).

The authors discuss the \(p\)-Dirichlet integral for mappings between compact Riemannian manifolds. The exponent \(p\) may be non-integer. The emphasis is on the role played by the geometry of the target manifold in the weak formulation of the variational problem on the appropriate Sobolev spaces.

Reviewer: G.Warnecke (Stuttgart)

MSC:

49Q20	Variational problems in a geometric measure-theoretic setting
58C99	Calculus on manifolds; nonlinear operators

Keywords:

concentrations; \(p\)-Dirichlet integral; compact Riemannian manifolds; variational problem; Sobolev spaces