The Best Constant in the Embedding of W N,1 (ℝ N ) into L ∞ (ℝ N )

Itai Shafrir

doi:10.1007/s11118-018-9695-5

The Best Constant in the Embedding of W ^N,1 (ℝ ^N ) into L ^∞ (ℝ ^N )

Itai Shafrir

Mathematics

Technion - Israel Institute of Technology

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

Abstract

We compute the best constant in the embedding of W ^N ^, ¹ (ℝ ^N ) into L ^∞ (ℝ ^N ) , extending a result of Humbert and Nazaret in dimensions one and two to any N. The main tool is the identification of log | x| as a fundamental solution of a certain elliptic operator of order 2N.

Original language	English
Pages (from-to)	581-590
Number of pages	10
Journal	Potential Analysis
Volume	50
Issue number	4
DOIs	https://doi.org/10.1007/s11118-018-9695-5
State	Published - 15 May 2019

Keywords

Best constant
Sobolev embedding

All Science Journal Classification (ASJC) codes

Analysis

Access to Document

10.1007/s11118-018-9695-5

Cite this

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abstract = " We compute the best constant in the embedding of W N , 1 (ℝ N ) into L ∞ (ℝ N ) , extending a result of Humbert and Nazaret in dimensions one and two to any N. The main tool is the identification of log | x| as a fundamental solution of a certain elliptic operator of order 2N.",

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