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We introduce integrands f : R nN → R of (s, µ, q)-type, which are, roughly speaking, of lower (upper) growth rate s ≥ 1 (q > 1) satisfying in additionwe prove partial C 1 -regularity of local minimizers u ∈ W 1 1,loc (Ω, R N ) by the way including integrands f being controlled by some N -function and also integrands of anisotropic power growth. Moreover, we extend the known results up to a certain limit and present examples which are not covered by the standard theory. (2000): 49 N 60, 49 N 99, 35 J 45 Mathematics Subject Classification

On removable singularities of p-harmonic maps Annales de l'I. H. P., section C, tome 7, n o 5 (1990), p. 385-405 © Gauthier-Villars, 1990, tous droits réservés. L'accès aux archives de la revue « Annales de l'I. H. P., section C » (http://www.elsevier.com/locate/anihpc) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

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We establish several smoothness results for local minimizers of nonautonomous variational integrals with anisotropic growth conditions.

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We investigate the smoothness properties of local solutions of the nonlinear Stokes problemwhere v: Ω → R n is the velocity field, π: Ω → R denotes the pressure function, and g: Ω → R n represents a system of volume forces, Ω denoting an open subset of R n . The tensor T is assumed to be the gradient of some potential f acting on symmetric matrices. Our main hypothesis imposed on f is the existence of exponents 1 < p ≤ q < ∞ such thatholds with suitable constants λ, Λ > 0, i.e. the potential f is of anisotropic power growth. Under natural assumptions on p and q we prove that velocity fields from the space W 1 p,loc (Ω; R n ) are of class C 1,α on an open subset of Ω with full measure. If n = 2, then the set of interior singularities is empty. Mathematics Subject Classification (2000). 76M30, 49N60, 35J50, 35Q30.