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arXiv · 2306.10995

Improved regularity for a Hessian-dependent functional

Vincenzo Bianca·Edgard A. Pimentel·José Miguel Urbano
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Abstract

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 H\"older regularity theory available for elliptic equations in double-divergence form.

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Vincenzo Bianca, Edgard A. Pimentel, José Miguel Urbano. 2023-06-19. Improved regularity for a Hessian-dependent functional. https://arxiv.org/abs/2306.10995

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