Weighted Korn inequality on John domains

2016/12/14 by Fernando López García, García, Fernando López · 1 citation
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1612.04445

openalex publication_date 2016/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show a weighted version of Korn inequality on bounded euclidean John domains, where the weights are nonnegative powers of the distance to the boundary. In this theorem, we also provide an estimate of the constant involved in the inequality which depends on the power that appears in the weight and a geometric condition that characterizes John domains. The proof uses a local-to-global argument based on a certain decomposition of functions. In addition, we prove the solvability in weighted Sobolev spaces of div(u)=f on the same class of domains. In this case, the weights are nonpositive powers of the distance to the boundary. The constant appearing in this problem is also estimated.

Citations

• An elementary proof of the continuity from L₀²(Ω) to H¹₀(Ω)ⁿ of Bogovskii's right inverse of the divergence

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• Weighted graphs in the sense of John and a global Poincaré inequality

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