More on Fundamental Solutions for Systems

Abstract

The issue of identifying fundamental solutions for homogeneous constant coefficient systems of arbitrary order is a central topic here. As particular cases of the approach is developed, fundamental solutions that are tempered distributions for the Lamé and Stokes operators are derived. The fact that integral representation formulas and interior estimates hold for null-solutions of homogeneous systems with nonvanishing full symbol is also proved. As a consequence, null-solutions are real-analytic and shown to satisfy reverse Hölder estimates. Finally, layer potentials associated with arbitrary constant coefficient second- order systems in the upper-half space, and the relevance of these operators vis-a-vis to the solvability of boundary value problems for such systems in this setting, are discussed.