(untitled) (Journal of Partial Differential Equations, 1997)
We prove partial regularity for minimizers of degenerate variational integrals ∫_Ω F(x, u, Du)dx with obstacles of either the form (i) μ_f = u ∈ H^1,m (Ω,R^N)|u^N ≥ f_1(u¹, ... ,u^N-1) + f_2(x) a.e. or (ii) μ_N = u ∈ H^1,m(Ω,R^N)|u^i(x) ≥ h^i(x), a.e.; i=1, ... ,N The typical mode of variational integrals is given by ∫_Ω [a^αβ(x, u)b_ij(x, u)D_αu^i D_βu^i]^m2 dx, m ≥ 2