Beltrami equations in the plane and Sobolev regularity
Beltrami equations in the plane and Sobolev regularity
New results regarding the Sobolev regularity of the principal solution of the linear Beltrami equation $\bar{\partial} f = μ \partial f + ν \overline{\partial f}$ for discontinuous Beltrami coefficients $μ$ and $ν$ are obtained, using Kato-Ponce commutators, obtaining that $\overline \partial f$ belongs to a Sobolev space with the same …