The Equality of Mixed Partial Derivatives Under Weak Differentiability Conditions

2015/01/01 by E. Minguzzi · 14 citations
Mathematics · #Advanced Differential Equations and Dynamical Systems #Analytic and geometric function theory #Differentiable function #Geometric Analysis and Curvature Flows #Mathematics #Pure mathematics

paper · doi:10.14321/realanalexch.40.1.0081

published in Real Analysis Exchange 40(1), 81 (Michigan State University Press)

openalex publication_date 2015/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/03/25

Abstract

We review and develop two little known results on the equality of mixed partial derivatives which can be considered the best results so far available in their respective domains. The former, due to Mikusi'nski and his school, deals with equality at a given point, while the latter, due to Tolstov, concerns equality almost everywhere. Applications to differential geometry and General Relativity are commented.

Citations

• Mixed Partial Derivatives and Fubini's Theorem

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• Symmetry of second derivatives [wikipedia]

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