Semigroups Connected with Parameter-elliptic Douglis-nirenberg Systems

Abstract

It was shown by Seeley that associated with a parameter-elliptic boundary problem involving a system of differential operators of homogeneous type there was associated an analytic semigroup. This result was extended by Dreher to a Douglis-Nirenberg system of mono-order type, i.e., the diagonal operators are all of the same order. In this paper we again discuss the problem considered by Dreher, but use a different approach as his approach gives rise to certain difficulties. We also extend the results for mono-order systems to a certain class of Douglis-Nirenberg systems of multiorder type, i.e., the diagonal operators are not all of the same order. 2010 Mathematics Subject Classification: 35J55; 47D06.