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Quantitative Hardness Measurement by Instrumented AFM-indentation
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Hardy type inequalities on the sphere.

Xiaomei Sun1, Fan Pan1

  • 1College of Science, Huazhong Agricultural University, Wuhan, 430070 China.

Journal of Inequalities and Applications
|July 7, 2017
PubMed
Summary
This summary is machine-generated.

This study establishes [Formula: see text]-Hardy inequalities on the sphere using the divergence theorem. It also provides the best constants for these inequalities, extending previous work.

Keywords:
Hardy type inequalitybest constantsphere

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Area of Science:

  • Mathematical Analysis
  • Geometric Analysis

Background:

  • Hardy inequalities are fundamental in analysis, with applications in partial differential equations and spectral theory.
  • The study of Hardy inequalities on manifolds, particularly spheres, is an active area of research.

Purpose of the Study:

  • To establish [Formula: see text]-Hardy inequalities on the sphere.
  • To determine the best constants associated with these inequalities.
  • To extend existing results in the field.

Main Methods:

  • Application of the divergence theorem on the sphere.
  • Analytical techniques to derive and verify inequalities.

Main Results:

  • Successful establishment of [Formula: see text]-Hardy inequalities on the sphere.
  • Derivation of the best possible constants for these inequalities.
  • Demonstration that the findings extend Xiao's prior work.

Conclusions:

  • The established [Formula: see text]-Hardy inequalities provide a significant contribution to the analysis on spheres.
  • The obtained best constants are crucial for understanding the sharpness of these inequalities.
  • This research advances the understanding of Hardy-type inequalities in geometric contexts.