A decomposition by non-negative functions in the Sobolev Space Wk,1

Augusto C. Ponce; Daniel Spector

doi:10.1512/iumj.2020.69.8237

A decomposition by non-negative functions in the Sobolev Space W^k,1

Augusto C. Ponce, Daniel Spector

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

4 Citations (Scopus)

Abstract

We show how a strong capacitary inequality can be used to give a decomposition of any function in the Sobolev space W^k,1(ℝ^d) as the difference of two non-negative functions in the same space with control of their norms.

Original language	English
Pages (from-to)	151-169
Number of pages	19
Journal	Indiana University Mathematics Journal
Volume	69
Issue number	1
DOIs	https://doi.org/10.1512/iumj.2020.69.8237
Publication status	Published - 2020
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1512/iumj.2020.69.8237

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abstract = "We show how a strong capacitary inequality can be used to give a decomposition of any function in the Sobolev space Wk,1(ℝd) as the difference of two non-negative functions in the same space with control of their norms.",

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A decomposition by non-negative functions in the Sobolev Space W^k,1

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