Nonnegative Whitney Extension Problem for C¹(ℝⁿ)

2019/12/13 by Jiang, Fushuai
#26B05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.06327

Abstract

Let f be a real-valued function on a compact subset in ℝⁿ . We show how to decide if f extends to a nonnegative and C¹ function on ℝⁿ . There has been no known result for nonnegative C^m extension from a general compact set E when m > 0 . The nonnegative extension problem for m ≥ 2 remains open.

Related

• Extension theorems of Whitney type by the use of integral operators
• The Whitney Extension Theorem for C¹, horizontal curves in the Heisenberg group
• Roots, trace, and extendability of flat nonnegative smooth functions
• The Whitney extension theorem in high dimensions
• On C¹ Whitney extension theorem in Banach spaces