The refinement and generalization of Hardy’s inequality in Sobolev space

In this paper, we refine the proof of Hardy’s inequality in (Evans in Partial Differential Equations, 2010, Hardy in Inequalities, 1952) and extend Hardy’s inequality from two aspects. That is to say, we extend the integral estimation function from [Formula: see text] to [Formula: see text] with sui...

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Detalles Bibliográficos
Autores principales: Xue, Xiaomin, Li, Fushan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6267400/
https://www.ncbi.nlm.nih.gov/pubmed/30839848
http://dx.doi.org/10.1186/s13660-018-1922-5
Descripción
Sumario:In this paper, we refine the proof of Hardy’s inequality in (Evans in Partial Differential Equations, 2010, Hardy in Inequalities, 1952) and extend Hardy’s inequality from two aspects. That is to say, we extend the integral estimation function from [Formula: see text] to [Formula: see text] with suitable [Formula: see text] and extend the space dimension from [Formula: see text] to [Formula: see text] . Hardy’s inequality in (Evans in Partial Differential Equations, 2010, Hardy in Inequalities, 1952) is the special case of our results.

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