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Boundary value problems for linear equations

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Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2,volume 2)

Abstract

In this chapter, after having introduced notation which will be constantly used in the course of our exposition, we shall indicate how to pose the various boundary value problems for linear elliptic equations of second order. Next we shall state uniqueness theorems for such problems which follow immediately from the maximum and minimum principles for the solutions. Introducing finally the concepts of Levi functions, fundamental solutions, and Green’s functions, we shall establish some fundamental integral formulas.

Keywords

  • Banach Space
  • Elliptic Equation
  • DIRICHLET Problem
  • Fundamental Solution
  • Regular Solution

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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  • DOI: 10.1007/978-3-642-87773-5_1
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© 1970 Springer-Verlag Berlin · Heidelberg

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Miranda, C. (1970). Boundary value problems for linear equations. In: Partial Differential Equations of Elliptic Type. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87773-5_1

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  • DOI: https://doi.org/10.1007/978-3-642-87773-5_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-87775-9

  • Online ISBN: 978-3-642-87773-5

  • eBook Packages: Springer Book Archive