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Functions represented by integrals

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

Abstract

In this chapter we shall occupy ourselves with the study of certain functions represented by either domain or surface integrals, with the purpose of establishing under what conditions such functions turn out to be integrable, or continuous, Hölder continuous, differentiable, etc. Among others, we shall study certain integrals which we can consider a natural extension of the ordinary potential either of a domain or of a single or double layer. This fact shows the importance of the contents of this chapter to the end of a systematic treatment of the theory of elliptic equations.

Keywords

  • Integral Sign
  • Direction Cosine
  • Layer Potential
  • Hyperplane Tangent
  • Distinct Limit

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Reference

  1. Evans, G.C. and E.R.C. Miles: Potential of general masses in single and double layers. The relative boundary value problems. Amer. J. Math. 53 (1931) 493–516.

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  2. E. Gagliardo: Caratterizzazione delle traccie sulla frontiera relative ad alcune classi di funzioni in n variabili. Rend. Sem. Mat. Padova 27 (1957), 284–305.

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© 1970 Springer-Verlag Berlin · Heidelberg

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Miranda, C. (1970). Functions represented by integrals. 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_2

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  • DOI: https://doi.org/10.1007/978-3-642-87773-5_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-87775-9

  • Online ISBN: 978-3-642-87773-5

  • eBook Packages: Springer Book Archive