The transformation of elliptic differential equations (with 2 independent variables) into the complex yields formal hyperbolic differential equations. These are solved by the integral operators of I.N. Vekua or St. Bergman or M. Eichler and by the differential operator of K.W. Bauer. Furthermore, a transformation law of general Bergman kernels and of Bergman kernels with the first kind is derived. The integral operators of Eichler and Bergman and the differential operators are generalized for partial differential equations with more than 2 variables and higher order than 2.
|Title of host publication||Solving methods of partial differential equations with second and higher order. Habilitation|
|Number of pages||234|
|Publication status||Published - 1989|