ON THE APPROXIMATE SOLUTION OF PROBLEMS IN MATHEMATICAL PHYSICS

Abstract

CONTENTS ??1. Introduction. Remarks on the method of the Fischer-Riesz equations ??2. Theorems on the completeness of systems of functions and on differential properties of solutions of integral equations ??3. Boundary-value problems for harmonic functions ??4. Boundary-value problems for biharmonic functions ??5. Boundary-value problems for metaharmonic functions. Diffraction of a sound wave ??6. Limiting problems for the equation of thermal conduction ??7. Boundary-value problems for the system of Maxwell's equations. Propagation of electromagnetic waves in a piecewise-inhomogeneous medium ??8. The fundamental boundary value problem in electrodynamics ??9. Remarks on the solution of some other problemsReferences