Zur Entwicklung von Randintegralgleichungen für eine Aufgabenklasse der mathematischen Physik. (Developing boundary integral equations for a class of problems of mathematical physics) (Q1117095)

The aim of this paper is to construct a unified approach for solving elliptic boundary value problems frequently appearing in engineering applications by integral methods. In this way a complete set of basic relations is set up in the framework of continuum theory. In general this theory encloses three types of basic equations, kinematic relations, equilibrium equations and constitutive equations. From this point of view a system of elliptic equations and related boundary conditions may be derived. This system is a linear one, including, e.g. elastostatistics and heat conduction phenomena. A direct boundary integral representation for the derived three-dimensional boundary value problem is given following standard techniques used for analysis. Resulting boundary integral equations are quite general, because the special analysis of the problem only appears in the fundamental solutions. Therefore any available boundary element code especially those for three-dimensional elasto-statics may be extended to general elliptic problems. Concerning the considered problems a general approach for derivation of fundamental solutions is presented.