Hardy type inequalities and parametric Lamb equation

2020/03/19 by R. V. Makarov, Makarov R. V., V., Makarov R. +2
Computer Science · Mathematics · #26D10 #26D15 #Analytic and geometric function theory #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #math.FA #msc:26D10 #msc:26D15

paper · pdf · doi:10.48550/arxiv.2003.08584

arxiv created 2020/03/19 · openalex publication_date 2020/03/19 · arxiv updated 2020/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to Hardy type inequalities with remainders for compactly supported smooth functions on open sets in the Euclidean space. We establish new inequalities with weight functions depending on the distance function to the boundary of the domain. One-dimensional L₁ and L_p inequalities and their multidimensional analogues are proved. We consider spatial inequalities in open convex domains with the finite inner radius. Constants in these inequalities depend on the roots of parametric Lamb equation for the Bessel function and turn out to be sharp in some particular cases.

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