Beltrami equations in the plane and Sobolev regularity

New results regarding the Sobolev regularity of the principal solution of the linear Beltrami equation (formula presented) Bf for discontinuous Beltrami coefficients μ and v are obtained, using Kato-Ponce commutators, obtaining that Bf belongs to a Sobolev space with the same smoothness as the coeff...

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Detalles Bibliográficos
Autor: Prats, Martí|||0000-0001-8799-6995
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:288652
Acceso en línea:https://ddd.uab.cat/record/288652
https://dx.doi.org/urn:doi:10.3934/cpaa.2018018
Access Level:acceso abierto
Palabra clave:Beltrami Equation
Fractional Derivatives
Kato-Ponce commutator
Quasiconformal Mappings
Sobolev Spaces
Descripción
Sumario:New results regarding the Sobolev regularity of the principal solution of the linear Beltrami equation (formula presented) Bf for discontinuous Beltrami coefficients μ and v are obtained, using Kato-Ponce commutators, obtaining that Bf 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.