Skip to main content
Log in

Mathematical theory of «points effect» in electricity conducting surfaces

  • Conferenze
  • Published:
Rendiconti del Seminario Matematico e Fisico di Milano Aims and scope Submit manuscript

Sunto

Vengono riportati i risultati ottenuti nel problema consistente nel determinare le proprietà qualitative della densità elettrica e del campo elettrico originati da una carica in equilibrio su una superficie chiusa. In particolare si studia il comportamento asintotico dell’una e dell’altro in prossimità delle punte e degli spigoli della superficie conduttrice.

Abstract

The paper is concerned with results obtained in the problem consisting in determining the qualitative properties of the electric density and of the electric field originated by a load in equilibrium on a closed surface. In particular the asymptotic behaviour of both of them near the points and the edges of the conducting surface are studied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Sneider M. A.,Sulla capacità elettrostatica di una superficie chiusa. Mem. Accad. Naz. Lincei VIII, X, 1970, pp. 97–215.

    Google Scholar 

  2. Petrovsky I. G.,Lectures on Partial Differential Equations. Interscience, New York, 1954.

    MATH  Google Scholar 

  3. Picone M.,Appunti di Analisi superiore. Rondinella Napoli, 1940.

  4. Fichera G.,Teoremi di completezza sulla frontiera di un dominio per taluni sistemi di funzioni. Ann. Matem. pura ed appl. IV, XXVII, 1948, pp. 1–28.

    Article  Google Scholar 

  5. Gunther N. M.,Die Pontentialtheorie. G. Teubner, Leipzig, 1957.

    Google Scholar 

  6. Gagliardo E.,Proprietà di alcune classi di funzioni in più variabili. Ricerche di Matem. VII, 1958, pp. 102–137.

    MathSciNet  Google Scholar 

  7. Fichera G.,Linear elliptic differential systems and eigenvalue problems. Lecture Notes in Mathematics 8, Springer, Heidelberg, 1965.

    MATH  Google Scholar 

  8. Castellani Rizzonelli P.,On the first boundary value problem for the classical theory of elasticity in a three-dimensional domain with a singular boundary. Jour. of Elasticity, 3, 4, 1973, pp. 225–259.

    Article  Google Scholar 

  9. Fichera G.,Asymptotic behaviour of the electric field and density of the electric charge in the neighborhood of singular points of a conducting surface (in russian). Uspekhi Mat. Nauk, 30: 3, 1975, pp. 105–124; English translation: Russian Math. Surveys, 30: 3, 1975, pp. 107–127; Ital. translation: Rend. Sem. Mat. Univ. Polit. Torino, 32, 1973–74, pp. 111–143.

    MATH  MathSciNet  Google Scholar 

  10. Courant R.Hilbert D.,Methods of Mathematical Physics. Vol. I, Interscience Publ., New York, 1953.

    Google Scholar 

  11. Fichera G.Sneider M. A.,Distribution de la charge électrique dans le voisinage des sommets et des arêtes d’un cube. C. R. Acad. Sci. Paris, 278 A, 1974, pp. 1303–1306.

    MATH  MathSciNet  Google Scholar 

  12. Fichera G.,Asymptotic behaviour of the electric field near the singular points of the conducting surface (in russian). Proceed. of the Conference in honour of I. G. Petrovski 75th Anniversary (Moscow 1976); Univ. of Moscow Publ. 1978, pp. 230–235. English transl.: Rend. Acc. Naz. Lincei, vol. LX, pp. 13–20.

Download references

Author information

Authors and Affiliations

Authors

Additional information

(Conferenza tenuta il 3 aprile 1979)

Il testo di questa conferenza è stato redatto in lingua inglese per consentire una maggiore diffusione degli argomenti in essa trattati.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fichera, G. Mathematical theory of «points effect» in electricity conducting surfaces. Seminario Mat. e. Fis. di Milano 49, 19–48 (1979). https://doi.org/10.1007/BF02925180

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02925180

Keywords

Navigation