Eigenvalue asymptotics for a boundary problem involving an elliptic system

In a recent paper, Agranovich, Denk, and Faierman developed a method for deriving results pertaining to the eigenvalue asymptotics for scalar elliptic boundary problems involving a weight function under limited smoothness assumptions and under an ellipicity with parameter condition. Denk, Faierman, and Möller then used this method to extend the aforementioned results for the scalar case to the case of a homogeneous elliptic systems. However, the method of Agranovich et al. does not carry over to more general elliptic systems of Agmon–Douglis–Nirenberg type. By employing a different method, we are able to overcome this difficulty, and hence in this paper we derive results pertaining to the eigenvalue asymptotics for more general systems of Agmon–Douglis–Nirenberg type and under limited smoothness assumptions. Furthermore, our results not only subsume those of Denk et al., but are derived under much weaker smoothness assumptions. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)