The simple layer potential for the biharmonic equation in n variables

Alberto Cialdea

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1991)

  • Volume: 2, Issue: 2, page 115-127
  • ISSN: 1120-6330

Abstract

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A theory of the «simple layer potential» for the classical biharmonic problem in R n is worked out. This hinges on the study of a new class of singular integral operators, each of them trasforming a vector with n scalar components into a vector whose components are n differential forms of degree one.

How to cite

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Cialdea, Alberto. "The simple layer potential for the biharmonic equation in \( n \) variables." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 2.2 (1991): 115-127. <http://eudml.org/doc/244337>.

@article{Cialdea1991,
abstract = {A theory of the «simple layer potential» for the classical biharmonic problem in \( \mathbb\{R\}^\{n\} \) is worked out. This hinges on the study of a new class of singular integral operators, each of them trasforming a vector with \( n \) scalar components into a vector whose components are \( n \) differential forms of degree one.},
author = {Cialdea, Alberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Singular integral operators; Differential forms; Biharmonic problem; biharmonic; simple layer potential; singular integral operators},
language = {eng},
month = {6},
number = {2},
pages = {115-127},
publisher = {Accademia Nazionale dei Lincei},
title = {The simple layer potential for the biharmonic equation in \( n \) variables},
url = {http://eudml.org/doc/244337},
volume = {2},
year = {1991},
}

TY - JOUR
AU - Cialdea, Alberto
TI - The simple layer potential for the biharmonic equation in \( n \) variables
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1991/6//
PB - Accademia Nazionale dei Lincei
VL - 2
IS - 2
SP - 115
EP - 127
AB - A theory of the «simple layer potential» for the classical biharmonic problem in \( \mathbb{R}^{n} \) is worked out. This hinges on the study of a new class of singular integral operators, each of them trasforming a vector with \( n \) scalar components into a vector whose components are \( n \) differential forms of degree one.
LA - eng
KW - Singular integral operators; Differential forms; Biharmonic problem; biharmonic; simple layer potential; singular integral operators
UR - http://eudml.org/doc/244337
ER -

References

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  8. FICHERA, G., Operatori di Riesz-Fredholm, operatori riducibili, equazioni integrali singolari, applicazioni. Pubbl. dell'Ist. Matem. dell'Univ. di Roma, 1963. 
  9. FICHERA, G., Linear Elliptic Differential Systems and Eigenvalue Problems. Lecture notes in mathematics, vol. 8, Springer, Berlin-Heidelberg-New York1965. Zbl0138.36104MR209639
  10. V. D. KUPRADZE (éd.), Three-dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity. North-Holland, Amsterdam1979. Zbl0406.73001MR530377
  11. MIKHLIN, S. G., Multidimensional Singular Integrals and Integral Equations. Pergamon Press, Oxford1965. Zbl0129.07701MR185399
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