Interior partial regularity for minimizers of functionals having nonquadratic growth between Riemannian manifolds has been extensively studied. See [2], [6], [8], [9] and references therein for details. Here we study sections of a fiber bundle X that locally minimize the L~p norm of the gradient among all L_(loc)~(1,p) sections when p ∈ (1, ∞).We show that such a local minimizing section is Hoelder continuous everywhere except a closed subset Z of the base manifold M, and that the set Z has Hausdorff dimension at most m — [p] — 1, where m is the dimension of M.
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