A boxing inequality for the fractional perimeter

AUGUSTO C. PONCE, Daniel Spector

研究成果: 雜誌貢獻期刊論文同行評審

8 引文 斯高帕斯(Scopus)

摘要

We prove the Boxing inequality (equation presented) for every α 2 (0, 1) and every bounded open subset U ⊂Rd , where Hd-α 1 (U) is the Hausdorff content of U of dimension d - α and the constant C >0 depends only on d. We then show how this estimate implies a trace inequality in the fractional Sobolev space Wα,1(Rd ) that includes Sobolev's L d d-α embedding, its Lorentz-space improvement, and Hardy's inequality. All these estimates are thus obtained with the appropriate asymptotics as α tends to 0 and 1, recovering in particular the classical inequalities of first order. Their counterparts in the full range α 2 (0, d) are also investigated.

原文英語
頁(從 - 到)107-141
頁數35
期刊Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
20
發行號1
DOIs
出版狀態已發佈 - 2020
對外發佈

ASJC Scopus subject areas

  • 理論電腦科學
  • 數學(雜項)

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