2005/10/27 by Tonia Ricciardi, Ricciardi, Tonia
Computer Science · Mathematics · #35J60 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP #msc:35J60
paper · pdf · doi:10.48550/arxiv.math/0510606
11 pages
arxiv created 2005/10/27 · openalex publication_date 2005/10/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We obtain an estimate for the Hölder continuity exponent for weak solutions to the following elliptic equation in divergence form: div(A(x)∇ u)=0 \qquadin\Ω, where Ω is a bounded open subset of \R2 and, for every x∈Ω, A(x) is a matrix with bounded measurable coefficients. Such an estimate "interpolates" between the well-known estimate of Piccinini and Spagnolo in the isotropic case A(x)=a(x)I, where a is a bounded measurable function, and our previous result in the unit determinant case det A(x)≡1. Furthermore, we show that our estimate is sharp. Indeed, for every τ∈[0,1] we construct coefficient matrices Aτ such that A0 is isotropic and A1 has unit determinant, and such that our estimate for Aτ reduces to an equality, for every τ∈[0,1].