One dimensional Weighted Hardy's Inequalities and application

2019/09/24 by Xiaojing Liu, Liu, Xiaojing, Toshio Horiuchi +3
Computer Science · Mathematics · #26D10 #34L30 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Primary 35J70 #Secondary 35J60

paper · pdf · doi:10.48550/arxiv.1909.10689

openalex publication_date 2019/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper we shall improve one dimensional weighted Hardy inequalities with one-sided boundary condition by adding sharp remainders. As an application, we shall establish n dimensional weighted Hardy inequalities in a bounded smooth domain with weight functions being powers of the distance function d(x) to the boundary. Our results will be applicable to variational problems in a coming paper.

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