Pointwise descriptions of nearly incompressible vector fields with bounded curl

2020/07/02 by Clop, Albert, Sengupta, Banhirup
#30C65 #30C99 #34A26 #35Q31 #42B37 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.00918

Abstract

Among those nearly incompressible vector fields \bfv:ℝⁿ→ℝⁿ with |x|log|x| growth at infinity, we give a pointwise characterization of the ones for which curl\bfv= D\bfv-D^t\bfv belongs to L^∞. When n=2 we can go further and describe, still in pointwise terms, the vector fields \bfv:ℝ²→ℝ² for which |div\bfv|+|curl\bfv|∈ L^∞.

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