arXiv:1606.07751 Abstract | arXiv Analytics

arXiv:1606.07751 [math.AP]Abstract References Reviews Resources

Beltrami equations in the plane and Sobolev regularity

Published 2016-06-24Version 1

Some new results regarding the Sobolev regularity of the principal solution of the linear Beltrami equation $\bar{\partial} f = \mu \partial f + \nu \bar{\partial f}$ for discontinuous Beltrami coefficients $\mu$ and $\nu$ are obtained, using Kato-Ponce commutators. A conjecture on the cases where the limitations of the method do not work is raised.

Comments: 16 pages, 12 figures

Categories: math.AP, math.CA

Subjects: 35J46, 30C62, 46L36

Keywords: sobolev regularity, linear beltrami equation, discontinuous beltrami coefficients, principal solution, kato-ponce commutators

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