Improved regularity for a Hessian-dependent functional

2023/06/19 by Vincenzo Bianca, Edgard A. Pimentel, Bianca, Vincenzo +3
Mathematics · #35B38 #49N60 #49Q20 #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2306.10995

openalex publication_date 2023/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We prove that minimizers of the L^d-norm of the Hessian in the unit ball of ℝ^d are locally of class C^1,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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