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

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.

MSC:

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