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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| 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 |
| 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. |
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