On a variational problem associated with a Hardy type inequality involving a mean oscillation

Norisuke Ioku; Michinori Ishiwata

doi:10.1007/s00526-015-0927-x

On a variational problem associated with a Hardy type inequality involving a mean oscillation

Norisuke Ioku, Michinori Ishiwata

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a minimizing problem associated with a critical Hardy type inequality involving a mean oscillation. We first introduce a dilation-invariant critical Hardy type inequality which contains a nonlocal term and then analyze the associated Euler–Lagrange equation with the aid of the scaling argument. We prove the nonexistence of minimizers for 1<p<∞ and the existence for p=1.

Original language	English
Pages (from-to)	3949-3966
Number of pages	18
Journal	Calculus of Variations and Partial Differential Equations
Volume	54
Issue number	4
DOIs	https://doi.org/10.1007/s00526-015-0927-x
Publication status	Published - 2015 Dec 1
Externally published	Yes

Keywords

46E35
Primary 26D10
Secondary 35J20

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s00526-015-0927-x

Cite this

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abstract = "We consider a minimizing problem associated with a critical Hardy type inequality involving a mean oscillation. We first introduce a dilation-invariant critical Hardy type inequality which contains a nonlocal term and then analyze the associated Euler–Lagrange equation with the aid of the scaling argument. We prove the nonexistence of minimizers for 1",

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On a variational problem associated with a Hardy type inequality involving a mean oscillation

Abstract

Keywords

ASJC Scopus subject areas

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