Second-order differentiability for solutions of elliptic equations in\n the plane

2013/03/13 by Vladimir Maz’ya, Maz'ya, Vladimir, Robert McOwen +1
Computer Science · Mathematics · #35J15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1303.3254

openalex publication_date 2013/03/13 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

For a second-order elliptic equation of nondivergence form in the plane, we\ninvestigate conditions on the coefficients which imply that all strong\nsolutions have first-order derivatives that are Lipschitz continuous or\ndifferentiable at a given point. We assume the coefficients have modulus of\ncontinuity satisfying the square-Dini condition, and obtain additional\nconditions associated with a dynamical system that is derived from the\ncoefficients of the elliptic equation. Our results extend those of previous\nauthors who assume the modulus of continuity satisfies the Dini condition.\n

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