Boundedness of the Hessian of a biharmonic function in a convex domain

2006/11/02 by Svitlana Mayboroda, Mayboroda, Svitlana, Vladimir Maz’ya +2
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP

paper · pdf · doi:10.48550/arxiv.math/0611058

openalex publication_date 2006/11/02 · arxiv created 2007/04/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Dirichlet problem for the biharmonic equation on an arbitrary convex domain and prove that the second derivatives of the variational solution are bounded in all dimensions.

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