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Introduction

  • Hermann Sohr
Chapter
  • 1.8k Downloads
Part of the Birkhäuser Advanced Texts Basler Lehrbücher book series (BAT)

Abstract

Throughout this book, Ω \( \Omega \subseteq \mathbb{R}^n \) n means a general domain, that is any open nonempty connected subset of the n-dimensional Euclidean space ℝ n . In the linearized theory we admit that n ≥ 2, the nonlinear theory is restricted to n = 2 and n = 3; in the preliminaries, see Chapters I and II, we sometimes admit the case n = 1. ∂Ω always means the boundary of Ω.Ω may be unbounded and ∂Ω may be also unbounded. In the sections on regularity properties, we suppose certain smoothness conditions on the boundary ∂Ω. The variables x = (x 1x n ) ∈ Ω are called space variables. T is always given with 0 < T ≤ ∞ and [0,T) is called the time interval; t ∈ [0,T) is called the time variable. We admit the case T = ∞.

Keywords

Weak Solution Strong Solution Lipschitz Domain Regularity Property Exterior Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2001

Authors and Affiliations

  • Hermann Sohr
    • 1
  1. 1.Fachbereich Mathematik/InformatikUniversität PaderbornPaderbornSwitzerland

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