Pointwise differentiability of higher-order for distributions

Ulrich Menne*

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

摘要

For distributions, we build a theory of higher-order pointwise differentiability comprising, for order zero, Łojasiewicz’s notion of point value. Results include Borel regularity of differentials, higher-order rectifiability of the associated jets, a Rademacher–Stepanov-type differentiability theorem, and a Lusin-type approximation. A substantial part of this development is new also for zeroth order. Moreover, we establish a Poincaré inequality involving the natural norms of negative order of differentiability. As a corollary, we characterise pointwise differentiability in terms of point values of distributional partial derivatives.

原文英語
頁(從 - 到)323-354
頁數32
期刊Analysis and PDE
14
發行號2
DOIs
出版狀態已發佈 - 2021

ASJC Scopus subject areas

  • 分析
  • 數值分析
  • 應用數學

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