Distributions. Sobolev Spaces

Abstract

We conclude this book with a glimpse at the means available for treating some unorthodox situations encountered in various areas of physics and engineering, in particular, in dynamics, electromagnetism, quantum field theory, and optimization. We here have in mind problems in which such classical requirements as the regularity and differentiability of functions, convergence of series, and smoothness of boundary conditions cannot be maintained, but must be relaxed, either in part or completely. This happens most frequently when we are concerned with temporal impulses (i.e., high intensity actions of very short duration), localized (concentrated) forces and couples acting on structural systems, point sources of various kinds, point masses, point charges, and finally, supports along lines or at isolated points.