We prove that minimizers of the L d Lᵈ -norm of the Hessian in the unit ball of R d R^d are locally of class C 1 , α C1,α . Our findings extend previous results on Hessian-dependent functionals to the borderline case and resonate with the Hölder regularity theory available for elliptic equations in double-divergence form.
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Bianca et al. (2024) studied this question.
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