| Abstract
| - We prove uniformcontinuity of radiallysymmetric vector minimizers uA( x) = UA(| x|) to multiple integrals ∫ B RL**( u( x), | Du( x)|) dx on a ballBR ⊂ ℝ d, among the Sobolev functions u(·) in A+ W01,1 ( B R, ℝ m), using a jointlyconvexlscL∗∗ : ℝ m×ℝ → [0,∞] with L∗∗( S,·) even and superlinear. Besides such basic hypotheses, L∗∗(·,·) is assumed to satisfy also a geometrical constraint, which we call quasi − scalar; the simplest example being the biradial case L∗∗(| u( x)|,| Du( x)|). Complete liberty is given for L∗∗( S,λ) to take the ∞ value, so that our minimization problem implicitly also represents e.g. distributed-parameter optimalcontrol problems, on constraineddomains, under PDEs or inclusions in explicit or implicit form. While generic radial functions u( x) = U(| x|) in this Sobolev space oscillate wildly as | x| → 0, our minimizing profile-curve UA(·) is, in contrast, absolutelycontinuous and tame, in the sense that its “ staticlevel” L∗∗( UA( r),0) always increases with r, a original feature of our result.
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