Improved regularity for a Hessian-dependent functional. (English) Zbl 07910789
Summary: We prove that minimizers of the \(L^d\)-norm of the Hessian in the unit ball of \(\mathbb{R}^d\) are locally of class \(C^{1,\alpha}\). 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.
MSC:
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35J35 | Variational methods for higher-order elliptic equations |
| 49N60 | Regularity of solutions in optimal control |
| 49Q20 | Variational problems in a geometric measure-theoretic setting |
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