On Cauchy estimates and growth orders of entire solutions of iterated Dirac and generalized Cauchy-Riemann equations

摘要

In this paper, we study the growth behaviour of entire Clifford algebra-valued solutions to iterated Dirac and generalized Cauchy-Riemann equations in higher-dimensional Euclidean space. Solutions to this type of systems of partial differential equations are often called k-monogenic functions or, more generically, polymonogenic functions. In the case dealing with the Dirac operator, the function classes of polyharmonic functions are included as particular subcases. These are important for a number of concrete problems in physics and engineering, such as, for example, in the case of the biharmonic equation for elasticity problems of surfaces and for the description of the stream function in the Stokes flow regime with high viscosity.