Improved Hardy inequalities with a class of weights

2022/09/27 by Anna Canale, Canale, Anna
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2209.13329

openalex publication_date 2022/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

\beginabstract In the paper we state conditions on potentials V to get the improved Hardy inequality with weight \beginsplit c_N,μ∫_\R^N(φ²)/(|x|²)μ(x)dxamp;+ ∫_\R^NV φ²μ(x)dx
amp;≤ ∫_\R^N|∇ φ|²μ(x)dx +K₁ ∫_\R^N φ²μ(x)dx, \endsplit for functions φ in a weighted Sobolev space and for weight functions μ of a quite general type. Some local improved Hardy inequalities are also given. To get the results we use a generalized vector field method. \endabstract

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