Beltrami equations in the plane and Sobolev regularity

Martí Prats

Beltrami equations in the plane and Sobolev regularity

Analysis of PDEs 2017-02-02 v3 Classical Analysis and ODEs

Authors: Martí Prats

Abstract

New results regarding the Sobolev regularity of the principal solution of the linear Beltrami equation $\bar{\partial} f = \mu \partial f + \nu \overline{\partial f}$ for discontinuous Beltrami coefficients $\mu$ and $\nu$ are obtained, using Kato-Ponce commutators, obtaining that $\overline \partial f$ 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.

Keywords

sobolev regularity of partial differential equations sobolev inequalities sobolev spaces

Cite

@article{arxiv.1606.07751,
  title  = {Beltrami equations in the plane and Sobolev regularity},
  author = {Martí Prats},
  journal= {arXiv preprint arXiv:1606.07751},
  year   = {2017}
}

Comments

13 pages, 12 figures

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