In this chapter, we will give a short overview on some basic concepts for the convenience of the reader. We start by introducing notation and summarize a few definitions as well as theorems from functional analysis, especially about linear operators, bilinear forms, and different kinds of function spaces, especially Sobolev spaces. Moreover, several characterizations of the regularity of domains are given and a few theorems from vector analysis (Gauß Theorem, Green’s Theorems, Reynold’s Transport Theorem) are recalled. The chapter concludes with some remarks on partial differential equations regarding classification and general theorems on the solvability of partial differential equations.


Linear Operator Sobolev Space Bilinear Form Lebesgue Space Weak Derivative 
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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Matthias Albert Augustin
    • 1
  1. 1.AG GeomathematikTechnische Universität KaiserslauternKaiserslauternGermany

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