Further results on the asymptotic growth of entire solutions of iterated Dirac equations in ℝn

✍ Scribed by D. Constales; R. De Almeida; R. S. Kraußhar

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 177 KB
• Volume: 29
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.689

✦ Synopsis

In this paper, we establish some further results on the asymptotic growth behaviour of entire solutions to iterated Dirac equations in R n . Solutions to this type of systems of partial di erential equations are often called polymonogenic or k-monogenic. In the particular cases where k is even, one deals with polyharmonic functions. These are of central importance for a number of concrete problems arising in engineering and physics, such as for example in the case of the biharmonic equation for the description of the stream function in the Stokes ow regime with low Reynolds numbers and for elasticity problems in plates.

The asymptotic study that we are going to perform within the context of these PDE departs from the Taylor series representation of their solutions. Generalizations of the maximum term and the central index serve as basic tools in our analysis.

By applying these tools we then establish explicit asymptotic relations between the growth behaviour of polymonogenic functions, the growth behaviour of their iterated radial derivatives and that of functions obtained by applying iterations of the operator to them.