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Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 3
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Original Articles

Gauged Sobolev inequalities

Umberto Mosco Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01-609, USACorrespondence[email protected]
Pages 367-402 | Received 11 Dec 2006, Accepted 21 Dec 2006, Published online: 13 Apr 2007
 
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Abstract

We present two-scale Morrey–Sobolev inequalities for measure-valued Lagrangeans on quasi-metric balls, scaled according to refined power laws. The fine tuning is given by suitable gauge functions, typically of logarithmic type. Fractal examples with fluctuating geometry are described.

†Dedicated to Ebba Swantje

Acknowledgement

The author wishes to thank Professor Maria Agostina Vivaldi for helpful discussions and useful comments on this work.

Notes

†Dedicated to Ebba Swantje

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