Beltrami equation
In mathematics, the Beltrami equation, named after Eugenio Beltrami, is the partial differential equation ∂ w ∂ z ¯ = μ ∂ w ∂ z . {\displaystyle {\frac {\partial w}{\partial {\bar {z}}}}=\mu {\frac {\partial w}{\partial z}}.} for w {\displaystyle w} a complex distribution of the complex variable z {\displaystyle z} in some open set U {\displaystyle U} , with derivatives that are locally L2, and where μ {\displaystyle \mu } is a given complex function in L∞(U) of norm less than 1, called the Beltrami coefficient, and where ∂ / ∂ z {\displaystyle \partial /\partial z} and ∂ / ∂ z ¯ {\displaystyle \partial /\partial {\bar {z}}} are Wirtinger derivatives.