Beltrami equations in the plane and Sobolev regularity

2016/06/24 by Prats, Martí
#30C62 #35J46 #46E35 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1606.07751

Abstract

New results regarding the Sobolev regularity of the principal solution of the linear Beltrami equation ∂ f = μ∂ f + ν∂ f for discontinuous Beltrami coefficients μ and ν are obtained, using Kato-Ponce commutators, obtaining that ∂ f belongs to a Sobolev space with the same smoothness as the coefficients but some loss in the integrability parameter. A conjecture on the cases where the limitations of the method do not work is raised.

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