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.
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Reference
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.
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
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